Hiroshi Suzuki | Last modified date：2021.06.22 |

Professor /
Fundamental particle physics /
Department of Physics /
Faculty of Sciences

**Papers**

1. | Hidenori Sonoda, Hiroshi Suzuki, Gradient flow exact renormalization group, Progress of Theoretical and Experimental Physics, https://doi.org/10.1093/ptep/ptab006, 2021, 2, 023B05, 2021.01, [URL]. |

2. | Kosuke Ishikawa, Okuto Morikawa, Akira Nakayama, Kazuya Shibata, Hiroshi Suzuki, Hiromasa Takaura, Infrared renormalon in the supersymmetric ℂP^{N-1} model on ℝ × S^{1}, Progress of Theoretical and Experimental Physics, 10.1093/ptep/ptaa002, 2020, 2, 2020.02, In the leading order of the large-N approximation, we study the renormalon ambiguity in the gluon (or, more appropriately, photon) condensate in the 2D supersymmetric ℂP model on ℝ × S with the ℤ twisted boundary conditions. In our large-N limit, the combination ΛR, where Λ is the dynamical scale and R is the S radius, is kept fixed (we set ΛR ≪ 1 so that the perturbative expansion with respect to the coupling constant at the mass scale 1/R is meaningful). We extract the perturbative part from the large-N expression of the gluon condensate and obtain the corresponding Borel transform B(u). For ℝ × S , we find that the Borel singularity at u = 2, which exists in the system on the uncompactified ℝ and corresponds to twice the minimal bion action, disappears. Instead, an unfamiliar renormalon singularity emerges at u = 3/2 for the compactified space ℝ × S . The semi-classical interpretation of this peculiar singularity is not clear because u = 3/2 is not dividable by the minimal bion action. It appears that our observation for the system on ℝ × S prompts reconsideration on the semi-classical bion picture of the infrared renormalon. N-1 1 1 1 2 1 1 N. |

3. | Masahiro Ashie, Okuto Morikawa, Hiroshi Suzuki, Hiromasa Takaura, Kengo Takeuchi, Infrared renormalon in SU(N) QCD(adj.) on ℝ^{3} × S^{1}, Progress of Theoretical and Experimental Physics, 10.1093/ptep/ptz157, 2020, 2, 2020.02, We study the infrared renormalon in the gluon condensate in the SU(N) gauge theory with n_{W}-flavor adjoint Weyl fermions (QCD(adj.)) on ℝ^{3}× S^{1} with the ℤ_{N} twisted boundary conditions. We rely on the so-called large-β_{0} approximation as a conventional tool to analyze the renormalon, in which only Feynman diagrams that dominate in the large-n_{W} limit are considered, while the coefficient of the vacuum polarization is set by hand to the one-loop beta function β_{0} = 11/3 2n_{W}/3. In the large N limit within the large-β_{0} approximation, the W-boson, which acquires the twisted Kaluza-Klein momentum, produces the renormalon ambiguity corresponding to the Borel singularity at u = 2. This provides an example that the system in the compactified space R^{3} × S^{1} possesses the renormalon ambiguity identical to that in the uncompactified space ℝ^{4}. We also discuss the subtle issue that the location of the Borel singularity can change depending on the order of two necessary operations.. |

4. | Kosuke Ishikawa, Okuto Morikawa, Kazuya Shibata, Hiroshi Suzuki, Hiromasa Takaura, Renormalon structure in compactified spacetime, Progress of Theoretical and Experimental Physics, 10.1093/ptep/ptz147, 2020, 1, 2020.01, We point out that the location of renormalon singularities in theory on a circle-compactified spacetime R^{d-1}} × S^{1} (with a small radius R Λ << 1) can differ from that on the non-compactified spacetime R^{d}. We argue this under the following assumptions, which are often realized in large N theories with twisted boundary conditions: (i) a loop integrand of a renormalon diagram is volume independent, i.e. it is not modified by the compactification, and (ii) the loop momentum variable along the S^{1} direction is not associated with the twisted boundary conditions and takes the values n/R with integer n. We find that the Borel singularity is generally shifted by-1/2 in the Borel u-plane, where the renormalon ambiguity of O(Λ^{k}) is changed to O(Λ^{k-1}/R) due to the circle compactification R^{d} → Rd^{-1} × S^{1}. The result is general for any dimension d and is independent of details of the quantities under consideration. As an example, we study the CP^{N-1}} model on R × S^{1} with Z_{N} twisted boundary conditions in the large-N limit.. |

5. | Hiroshi Suzuki, Hiromasa Takaura, Renormalon-free definition of the gluon condensate within the large-β0 approximation, Progress of Theoretical and Experimental Physics, 10.1093/ptep/ptz100, 2019, 10, 2019.10, We propose a clear definition of the gluon condensate within the large-β0 approximation as an attempt toward a systematic argument on the gluon condensate. We define the gluon condensate such that it is free from a renormalon uncertainty, consistent with the renormalization scale independence of each term of the operator product expansion (OPE), and an identical object irrespective of observables. The renormalon uncertainty of O(Λ4), which renders the gluon condensate ambiguous, is separated from a perturbative calculation by using a recently suggested analytic formulation. The renormalon uncertainty is absorbed into the gluon condensate in the OPE, which makes the gluon condensate free from the renormalon uncertainty. As a result, we can define the OPE in a renormalon-free way. Based on this renormalon-free OPE formula, we discuss numerical extraction of the gluon condensate using the lattice data of the energy density operator defined by the Yang-Mills gradient flow.. |

6. | Renormalon-free definition of the gluon condensate within the large-β0 approximation We propose a clear definition of the gluon condensate within the large-β0 approximation as an attempt toward a systematic argument on the gluon condensate. We define the gluon condensate such that it is free from a renormalon uncertainty, consistent with the renormalization scale independence of each term of the operator product expansion (OPE), and an identical object irrespective of observables. The renormalon uncertainty of O(Λ4), which renders the gluon condensate ambiguous, is separated from a perturbative calculation by using a recently suggested analytic formulation. The renormalon uncertainty is absorbed into the gluon condensate in the OPE, which makes the gluon condensate free from the renormalon uncertainty. As a result, we can define the OPE in a renormalon-free way. Based on this renormalon-free OPE formula, we discuss numerical extraction of the gluon condensate using the lattice data of the energy density operator defined by the Yang-Mills gradient flow.. |

7. | , Yusuke Taniguchi, Shinji Ejiri, Ryo Iwami, Kazuyuki Kanaya, Masakiyo Kitazawa, Hiroshi Suzuki, Hiroshi Suzuki, Naoki Wakabayashi, Erratum Exploring Nf=2+1 QCD thermodynamics from the gradient flow (Physical Review D (2017) 96 (014509) DOI: 10.1103/PhysRevD.99.014509), Physical Review D, 10.1103/PhysRevD.99.059904, 99, 5, 2019.03, Equation (C7) in the Appendix should read (Formula Presented) The wrong expression is not used in our numerical simulations and any results are not affected by this typo.. |

8. | Hidenori Sonoda, Hiroshi Suzuki, Derivation of a gradient flow from the exact renormalization group, Progress of Theoretical and Experimental Physics, 10.1093/ptep/ptz020, 2019, 3, 2019.03, We establish a concrete correspondence between a gradient flow and the renormalization group flow for a generic scalar field theory. We use the exact renormalization group formalism with a particular choice of the cutoff function.. |

9. | Takumi Iritani, Masakiyo Kitazawa, Hiroshi Suzuki, Hiromasa Takaura, Thermodynamics in quenched QCD Energy-momentum tensor with two-loop order coefficients in the gradient-flow formalism, Progress of Theoretical and Experimental Physics, 10.1093/ptep/ptz001, 2019, 2, 2019.02, Have computed the two-loop order (i.e., NNLO) coefficients in the gradient-flow representation of the energy-momentum tensor (EMT) in vector-like gauge theories. In this paper, we study the effect of the two-loop order corrections (and the three-loop order correction for the trace part of the EMT, which is available through the trace anomaly) on the lattice computation of thermodynamic quantities in quenched QCD. The use of the two-loop order coefficients generally reduces the t dependence of the expectation values of the EMT in the gradient-flow representation, where t is the flow time. With the use of the two-loop order coefficients, therefore, the t → 0 extrapolation becomes less sensitive to the fit function, the fit range, and the choice of the renormalization scale; the systematic error associated with these factors is considerably reduced.. |

10. | Okuto Morikawa, Hiroshi Suzuki, Numerical study of the N=2 Landau-Ginzburg model, Progress of Theoretical and Experimental Physics, 10.1093/ptep/pty088, 2018, 8, 2018.08, It is believed that the two-dimensional massless N = 2 Wess-Zumino model becomes the N = 2 superconformal field theory (SCFT) in the infrared (IR) limit. We examine this theoretical conjecture of the Landau-Ginzburg (LG) description of the N = 2 SCFT by numerical simulations on the basis of a supersymmetric-invariant momentum-cutoff regularization. We study a single supermultiplet with cubic and quartic superpotentials. From two-point correlation functions in the IR region, we measure the scaling dimension and the central charge, which are consistent with the conjectured LG description of the A2 and A3 minimal models, respectively. Our result supports the theoretical conjecture and, at the same time, indicates a possible computational method of correlation functions in the N = 2 SCFT from the LG description.. |

11. | Okuto Morikawa, Hiroshi Suzuki, Axial U(1) anomaly in a gravitational field via the gradient flow, Progress of Theoretical and Experimental Physics, 10.1093/ptep/pty073, 2018, 7, 2018.07, A regularization-independent universal formula for the energy-momentum tensor in gauge theory in the flat spacetime can be written down by employing the so-called Yang-Mills gradient flow. We examine a possible use of the formula in the calculation of the axial U(1) anomaly in a gravitational field, the anomaly first obtained by Toshiei Kimura [Prog. Theor. Phys. 42, 1191 (1969)]. As a general argument indicates, the formula reproduces the correct non-local structure of the (axial U(1) current)-(energy-momentum tensor)-(energy-momentum tensor) triangle diagram in a way that is consistent with the axial U(1) anomaly. On the other hand, the formula does not automatically reproduce the general coordinate (or translation) Ward-Takahashi relation, requiring corrections by local counterterms. This analysis thus illustrates the fact that the universal formula as it stands can be used only in on-shell correlation functions, in which the energy-momentum tensor does not coincide with other composite operators in coordinate space.. |

12. | Hiroki Makino, Okuto Morikawa, Hiroshi Suzuki, Gradient flow and the Wilsonian renormalization group flow, Progress of Theoretical and Experimental Physics, 10.1093/ptep/pty050, 2018, 5, 2018.05, The gradient flow is the evolution of fields and physical quantities along a dimensionful parameter t, the flow time. We give a simple argument that relates this gradient flow and the Wilsonian renormalization group (RG) flow. We then illustrate the Wilsonian RG flow on the basis of the gradient flow in two examples that possess an infrared fixed point, the 4D many-flavor gauge theory and the 3D O(N) linear sigma model.. |

13. | Kenji Hieda, Aya Kasai, Hiroki Makino, Hiroshi Suzuki, 4D N = 1 SYM supercurrent on the lattice in terms of the gradient flow, 35th International Symposium on Lattice Field Theory, Lattice 2017
EPJ Web of Conferences, 10.1051/epjconf/201817511014, 175, 2018.03, The gradient flow [1-5] gives rise to a versatile method to construct renor-malized composite operators in a regularization-independent manner. By adopting this method, the authors of Refs. [6-9] obtained the expression of Noether currents on the lattice in the cases where the associated symmetries are broken by lattice regularization. We apply the same method to the Noether current associated with supersymmetry, i.e., the supercurrent. We consider the 4D N = 1 super Yang-Mills theory and calculate the renormalized supercurrent in the one-loop level in the Wess-Zumino gauge. We then re-express this supercurrent in terms of the flowed gauge and flowed gaugino fields [10].. |

14. | Yusuke Taniguchi, Shinji Ejiri, Kazuyuki Kanaya, Masakiyo Kitazawa, Asobu Suzuki, Hiroshi Suzuki, Takashi Umeda, Energy-momentum tensor correlation function in N_{f} = 2 + 1 full QCD at finite temperature, 35th International Symposium on Lattice Field Theory, Lattice 2017
EPJ Web of Conferences, 10.1051/epjconf/201817507013, 175, 2018.03, We measure correlation functions of the nonperturbatively renormalized energy-momentum tensor in N_{f} = 2 + 1 full QCD at finite temperature by applying the gradient flow method both to the gauge and quark fields. Our main interest is to study the conservation law of the energy-momentum tensor and to test whether the linear response relation is properly realized for the entropy density. By using the linear response relation we calculate the specific heat from the correlation function. We adopt the nonperturba-tively improved Wilson fermion and Iwasaki gauge action at a fine lattice spacing = 0:07 fm. In this paper the temperature is limited to a single value T ? 232 MeV. The u, d quark mass is rather heavy with m_{π}=m_{ρ} ? 0:63 while the s quark mass is set to approximately its physical value.. |

15. | Kazuyuki Kanaya, Shinji Ejiri, Ryo Iwami, Masakiyo Kitazawa, Hiroshi Suzuki, Yusuke Taniguchi, Takashi Umeda, Equation of state in (2+1)-flavor QCD at physical point with improved Wilson fermion action using gradient flow, 35th International Symposium on Lattice Field Theory, Lattice 2017
EPJ Web of Conferences, 10.1051/epjconf/201817507023, 175, 2018.03, We study the energy-momentum tensor and the equation of state as well as the chiral condensate in (2+1)-flavor QCD at the physical point applying the method of Makino and Suzuki based on the gradient flow. We adopt a nonperturbatively O(a)- improved Wilson quark action and the renormalization group-improved Iwasaki gauge action. At Lattice 2016, we have presented our preliminary results of our study in (2+1)- flavor QCD at a heavy u; d quark mass point. We now extend the study to the physical point and perform finite-temperature simulations in the range T ? 155.544 MeV (N_{t} = 4-14 including odd N_{t}'s) at a ? 0:09 fm. We show our final results of the heavy QCD study and present some preliminary results obtained at the physical point so far.. |

16. | Hiroki Makino, Okuto Morikawa, Hiroshi Suzuki, One-loop perturbative coupling of A and A? through the chiral overlap operator, 35th International Symposium on Lattice Field Theory, Lattice 2017
EPJ Web of Conferences, 10.1051/epjconf/201817511013, 175, 2018.03, Recently, Grabowska and Kaplan constructed a four-dimensional lattice formulation of chiral gauge theories on the basis of the chiral overlap operator. At least in the tree-level approximation, the left-handed fermion is coupled only to the original gauge field A, while the right-handed one is coupled only to the gauge field A_{∗}, a deformation of A by the gradient flow with infinite flow time. In this paper, we study the fermion one-loop effective action in their formulation. We show that the continuum limit of this effective action contains local interaction terms between A and A _{∗}, even if the anomaly cancellation condition is met. These non-vanishing terms would lead an undesired perturbative spectrum in the formulation.. |

17. | Mizuki Shirogane, Shinji Ejiri, Ryo Iwami, Kazuyuki Kanaya, Masakiyo Kitazawa, Hiroshi Suzuki, Yusuke Taniguchi, Takashi Umeda, Equation of state near the first order phase transition point of SU(3) gauge theory using gradient flow, 36th Annual International Symposium on Lattice Field Theory, LATTICE 2018
Proceedings of Science, 334, 2018.01, We study energy gap (latent heat) between the hot and cold phases at the first order phase transition point of the SU(3) gauge theory. Performing simulations on lattices with various spatial volumes and lattice spacings, we calculate the energy gap by a method using the Yang-Mills gradient flow and compare it with that by the conventional derivative method.. |

18. | Atsushi Baba, Asobu Suzuki, Shinji Ejiri, Kazuyuki Kanaya, Masakiyo Kitazawa, Takanori Shimojo, Hiroshi Suzuki, Yusuke Taniguchi, Takashi Umeda, Measuring of chiral susceptibility using gradient flow, 36th Annual International Symposium on Lattice Field Theory, LATTICE 2018
Proceedings of Science, 334, 2018.01, In lattice QCD with Wilson-type quarks, the chiral symmetry is explicitly broken by the Wilson term on finite lattices. Though the symmetry is guaranteed to recover in the continuum limit, a series of non-trivial procedures are required to recover the correct renormalized theory in the continuum limit. Recently, a new use of the gradient flow technique was proposed, in which correctly renormalized quantities are evaluated in the vanishing flow-time limit. This enables us to directly study the chiral condensate and its susceptibility with Wilson-type quarks. Extending our previous study of the chiral condensate and its disconnected susceptibility in (2+1)-flavor QCD at a heavy u, d quark mass (m_{π} /m_{ρ} ≃ 0.63) and approximately physical s quark mass, we compute the connected contributions to the chiral susceptibility in the temperature range of 178–348 MeV on a fine lattice with a ≃ 0.07 fm.. |

19. | Yusuke Taniguchi, Atsushi Baba, Asobu Suzuki, Shinji Ejiri, Kazuyuki Kanaya, Masakiyo Kitazawa, Takanori Shimojo, Hiroshi Suzuki, Takashi Umeda, Study of energy-momentum tensor correlation function in N_{f} = 2 + 1 full QCD for QGP viscosities, 36th Annual International Symposium on Lattice Field Theory, LATTICE 2018
Proceedings of Science, 334, 2018.01, We study correlation functions of the energy-momentum tensor (EMT) in (2 + 1)-flavor full QCD to evaluate QGP viscosities. We adopt nonperturbatively improved Wilson fermion and Iwasaki gauge action. Our degenerate u, d quark mass is rather heavy with m_{π} /m_{ρ} ' 0.63, while the s quark mass is set to approximately its physical value. Performing simulations on lattices with N_{t} = 16 to 6 at a fine lattice spacing of a = 0.07 fm, the temperature range of T ' 174–464 MeV is covered using the fixed-scale approach. We attempt to compute viscosities by three steps: (1) calculate two point correlation functions of non-perturbatively renormalized EMT applying the gradient flow method, (2) derive the spectral function from correlation function, and (3) extract viscosities from the spectral function applying the Kubo formula. We report on the status of the project and present preliminary results for the shear viscosity in the high temperature phase.. |

20. | , Yusuke Taniguchi, Shinji Ejiri, Ryo Iwami, Kazuyuki Kanaya, Masakiyo Kitazawa, Hiroshi Suzuki, Takashi Umeda, Naoki Wakabayashi, Exploring Nf=2+1 QCD thermodynamics from the gradient flow, Physical Review D, 10.1103/PhysRevD.96.014509, 96, 1, 2017.07, The energy-momentum tensor plays an important role in QCD thermodynamics. Its expectation value contains information of the pressure and the energy density as its diagonal part. Further properties like viscosity and specific heat can be extracted from its correlation function. A nonperturbative evaluation of it on the lattice is called. Recently, a new method based on the gradient flow was introduced to calculate the energy-momentum tensor on the lattice and has been successfully applied to quenched QCD. In this paper, we apply the gradient flow method to calculate the energy-momentum tensor in (2+1)-flavor QCD adopting a nonperturbatively O(a)-improved Wilson quark action and the renormalization group-improved Iwasaki gauge action. As the first application of the method with dynamical quarks, we study at a single but fine lattice spacing a≃0.07 fm with heavy u and d quarks (mπ/mρ≃0.63) and approximately physical s quark (mηss/mφ≃0.74). With the fixed-scale approach, temperature is varied by the temporal lattice size Nt at a fixed lattice spacing. Performing simulations on lattices with Nt=16 to 4, the temperature range of T≃174-697 MeV is covered. We find that the results of the pressure and the energy density by the gradient flow method are consistent with the previous results using the T-integration method at T280 MeV (Nt10), while the results show disagreement at T350 MeV (Nt8), presumably due to the small-Nt lattice artifact of O((aT)2)=O(1/Nt2). We also apply the gradient flow method to evaluate the chiral condensate taking advantage of the gradient flow method that renormalized quantities can be directly computed avoiding the difficulty of explicit chiral violation with lattice quarks. We compute the renormalized chiral condensate in the MS- scheme at renormalization scale μ=2 GeV with a high precision to study the temperature dependence of the chiral condensate and its disconnected susceptibility. Even with the Wilson-type quark action which violates the chiral symmetry explicitly, we obtain the chiral condensate and its disconnected susceptibility showing a clear signal of pseudocritical temperature at T∼190 MeV related to the chiral restoration crossover.. |

21. | Kenji Hieda, Aya Kasai, Hiroki Makino, Hiroshi Suzuki, 4D N = 1 SYM supercurrent in terms of the gradient flow, Progress of Theoretical and Experimental Physics, 10.1093/ptep/ptx073, 2017, 6, 2017.06, The gradient flow and its small flow-time expansion provide a very versatile method to represent renormalized composite operators in a regularization-independent manner. This technique has been utilized to construct typical Noether currents such as the energy-momentum tensor and the axial-vector current in lattice gauge theory. In this paper, we apply the same technique to the supercurrent in the four-dimensional N = 1 super Yang-Mills theory (4D N = 1 SYM) in theWess-Zumino gauge. Since this approach provides a priori a representation of the properly normalized conserved supercurrent, our result should be useful, e.g., in lattice numerical simulations of the 4D N = 1 SYM; the conservation of the so-constructed supercurrent can be used as a criterion for the supersymmetric point toward which the gluino mass is tuned.. |

22. | Hiroki Makino, Okuto Morikawa, Hiroshi Suzuki, One-loop perturbative coupling of A and A _{∗}through the chiral overlap operator, Progress of Theoretical and Experimental Physics, 10.1093/ptep/ptx085, 2017, 6, 2017.06, We study the one-loop effective action defined by the chiral overlap operator in the fourdimensional lattice formulation of chiral gauge theories by Grabowska and Kaplan. In the tree-level continuum limit, the left-handed component of the fermion is coupled only to the original gauge field A, while the right-handed one is coupled only to A∗, which is given by the gradient flow of A with infinite flow time. In this paper, we show that the continuum limit of the one-loop effective action contains local interaction terms between A and A∗, which do not generally vanish even if the gauge representation of the fermion is anomaly free.We argue that the presence of such interaction terms can be regarded as undesired gauge symmetry-breaking effects in the formulation.. |

23. | One-loop perturbative coupling of A and A © The Author(s) 2017. We study the one-loop effective action defined by the chiral overlap operator in the fourdimensional lattice formulation of chiral gauge theories by Grabowska and Kaplan. In the tree-level continuum limit, the left-handed component of the fermion is coupled only to the original gauge field A, while the right-handed one is coupled only to A∗, which is given by the gradient flow of A with infinite flow time. In this paper, we show that the continuum limit of the one-loop effective action contains local interaction terms between A and A∗, which do not generally vanish even if the gauge representation of the fermion is anomaly free.We argue that the presence of such interaction terms can be regarded as undesired gauge symmetry-breaking effects in the formulation.. |

24. | Kenji Hieda, Hiroki Makino, Hiroshi Suzuki, Proof of the renormalizability of the gradient flow, Nuclear Physics B, 10.1016/j.nuclphysb.2017.02.017, 918, 23-51, 2017.05, We give an alternative perturbative proof of the renormalizability of the system defined by the gradient flow and the fermion flow in vector-like gauge theories.. |

25. | , Yusuke Taniguchi, Kazuyuki Kanaya, Hiroshi Suzuki, Takashi Umeda, Topological susceptibility in finite temperature (2+1)-flavor QCD using gradient flow, Physical Review D, 10.1103/PhysRevD.95.054502, 95, 5, 2017.03, We compute the topological charge and its susceptibility in finite temperature (2+1)-flavor QCD on the lattice applying a gradient flow method. With the Iwasaki gauge action and nonperturbatively O(a)-improved Wilson quarks, we perform simulations on a fine lattice with a≃0.07 fm at a heavy u, d quark mass with mπ/mρ≃0.63, but approximately physical s quark mass with mηss/mφ≃0.74. In a temperature range from T≃174 MeV (Nt=16) to 697 MeV (Nt=4), we study two topics on the topological susceptibility. One is a comparison of gluonic and fermionic definitions of the topological susceptibility. Because the two definitions are related by chiral Ward-Takahashi identities, their equivalence is not trivial for lattice quarks which violate the chiral symmetry explicitly at finite lattice spacings. The gradient flow method enables us to compute them without being bothered by the chiral violation. We find a good agreement between the two definitions with Wilson quarks. The other is a comparison with a prediction of the dilute instanton gas approximation, which is relevant in a study of axions as a candidate of the dark matter in the evolution of the Universe. We find that the topological susceptibility shows a decrease in T which is consistent with the predicted χt(T)(T/Tpc)-8 for three-flavor QCD even at low temperature Tpc |

26. | Hiroshi Suzuki, Energy-momentum tensor on the lattice Recent developments, Proceedings of Science, Part F128557, 2017.03, It is conceivable that the construction of the energy-momentum tensor (EMT) in lattice field theory enlarges our ability in lattice field theory and also deepens our understanding on EMT at the non-pertubative level. In this talk, I will review recent developments in this enterprise.. |

27. | Kazuyuki Kanaya, Shinji Ejiri, Ryo Iwami, Masakiyo Kitazawa, Hiroshi Suzuki, Yusuke Taniguchi, Takashi Umeda, Naoki Wakabayashi, Equation of state in (2+1)-flavor QCD with gradient flow, Proceedings of Science, Part F128557, 2017.03, The energy-momentum tensor and equation of state are studied in finite-temperature (2+1)-flavor QCD with improved Wilson quarks using the method proposed by Makino and Suzuki based on the gradient flow. We find that the results of the gradient flow are consistent with the previous results using the T-integration method at T <_{∼} 280MeV (Nτ > _{∼} 10), while a disagreement is found at T > _{∼} 350MeV (Nτ < _{∼} 8) presumably due to the small-Nτ lattice artifact. We also report on the results on the renormalized chiral condensate and its disconnected susceptibility using the method of Hieda and Suzuki. The results show a clear signal of the expected chiral restoration crossover even with Wilson-type quarks which violate the chiral symmetry explicitly.. |

28. | Masakiyo Kitazawa, Takumi Iritani, Masayuki Asakawa, Tetsuo Hatsuda, Hiroshi Suzuki, Equation of state for SU(3) gauge theory via the energy-momentum tensor under gradient flow, Physical Review D, 10.1103/PhysRevD.94.114512, 94, 11, 2016.12, The energy density and the pressure of SU(3) gauge theory at finite temperature are studied by direct lattice measurements of the renormalized energy-momentum tensor obtained by the gradient flow. Numerical analyses are carried out with β=6.287-7.500 corresponding to the lattice spacing a=0.013-0.061 fm. The spatial (temporal) sizes are chosen to be Ns=64, 96, 128 (Nτ=12, 16, 20, 22, 24) with the aspect ratio, 5.33≤Ns/Nτ≤8. Double extrapolation, a→0 (the continuum limit) followed by t→0 (the zero flow-time limit), is taken using the numerical data. Above the critical temperature, the thermodynamic quantities are obtained with a few percent precision including statistical and systematic errors. The results are in good agreement with previous high-precision data obtained by using the integral method.. |

29. | Kenji Hieda, Hiroshi Suzuki, Small flow-time representation of fermion bilinear operators, Modern Physics Letters A, 10.1142/S021773231650214X, 31, 38, 2016.12, Fermion bilinear operators of mass dimension 3, such as the axial-vector and vector currents, the pseudo-scalar and scalar densities, whose normalizations are fixed by Ward-Takahashi (WT) relations, are related to small flow-time behavior of composite operators of fermion fields evolved by Lüscher's flow equation. The representations can be useful in lattice numerical simulations, as recently demonstrated by the WHOT QCD collaboration for the chiral condensation of the N_{f} = 2 + 1 quantum chromodynamics (QCD) at finite temperature.. |

30. | Ken Ichi Okumura, Hiroshi Suzuki, Fermion number anomaly with the fluffy mirror fermion, Progress of Theoretical and Experimental Physics, 10.1093/ptep/ptw167, 2016, 12, 2016.12, Quite recently, Grabowska and Kaplan presented a 4-dimensional lattice formulation of chiral gauge theories based on the chiral overlap operator. We study this formulation from the perspective of the fermion number anomaly and possible associated phenomenology. A simple argument shows that the consistency of the formulation implies that the fermion with the opposite chirality to the physical one, the “fluffy mirror fermion” or “fluff”, suffers from the fermion number anomaly in the same magnitude (with the opposite sign) as the physical fermion. This immediately shows that if at least one of the fluff quarks is massless, the formulation provides a simple viable solution to the strong CP problem. Also, if the fluff interacts with gravity essentially in the same way as the physical fermion, the formulation can realize the asymmetric dark matter scenario.. |

31. | Etsuko Itou, Hiroshi Suzuki, Yusuke Taniguchi, Takashi Umeda, (2+1)-flavor QCD thermodynamics from the gradient flow, Proceedings of Science, 14-18-July-2015, 2016.07, Recently, we proposed a novel method to define and calculate the energy-momentum tensor (EMT) in lattice gauge theory on the basis of the Yang-Mills gradient flow [1]. In this pro- ceedings, we summarize the basic idea and technical steps to obtain the bulk thermodynamic quantities in lattice gauge theory using this method for the quenched and (2+1)-flavor QCD. The revised results of integration measure (trace anomaly) and entropy density of the quenched QCD with corrected coefficients are shown. Furthermore, we also show the flow time dependence of the parts of EMT including the dynamical fermions. This work is based on a joint-collaboration between FlowQCD and WHOT QCD.. |

32. | Hisashi Iha, Hiroki Makino, Hiroshi Suzuki, Upper bound on the mass anomalous dimension in many-flavor gauge theories A conformal bootstrap approach, Progress of Theoretical and Experimental Physics, 10.1093/ptep/ptw046, 2016, 5, 2016.05, We study four-dimensional conformal field theories with an SU(N) global symmetry by employing the numerical conformal bootstrap. We consider the crossing relation associated with a four-point function of a spin 0 operator ø^{k} _{i} which belongs to the adjoint representation of SU(N). For N = 12 for example, we found that the theory contains a spin 0 SU(12)-breaking relevant operator when the scaling dimension of Ø^{k} _{i}, δ Ø^{k} _{i}, is smaller than 1.71. Considering the lattice simulation of many-flavor quantum chromodynamics with 12 flavors on the basis of the staggered fermion, the above SU(12)-breaking relevant operator, if it exists, would be induced by the flavor-breaking effect of the staggered fermion and prevent an approach to an infrared fixed point. Actual lattice simulations do not show such signs. Thus, assuming the absence of the above SU(12)-breaking relevant operator, we have an upper bound on the mass anomalous dimension at the fixed point γ^{∗} _{m} ≤ 1.29 from the relation γ^{∗} _{m}, = 3 - δ Ø^{k} _{i}, Our upper bound is not so strong practically but it is strict within the numerical accuracy. We also find a kink-like behavior in the boundary curve for the scaling dimension of another SU(12)-breaking operator.. |

33. | Shinji Ejiri, Ryo Iwami, Mizuki Shirogane, Naoki Wakabayashi, Kazuyuki Kanaya, Masakiyo Kitazawa, Hiroshi Suzuki, Yusuke Taniguchi, Takashi Umeda, Determination of latent heat at the finite temperature phase transition of SU(3) gauge theory, Proceedings of Science, Part F128557, 2016.01, We calculate the energy gap (latent heat) and pressure gap between the hot and cold phases of the SU(3) gauge theory at the first order deconfining phase transition point. We perform simulations around the phase transition point with the lattice size in the temporal direction Nτ =6; 8 and 12 and extrapolate the results to the continuum limit. The energy density and pressure are evaluated by the derivative method with nonperturabative anisotropy coefficients. We find that the pressure gap vanishes at all values of Nt. The spatial volume dependence in the latent heat is found to be small on large lattices. Performing extrapolation to the continuum limit, we obtain Δϵ=T^{4} =0:75±0:17 and δ(ϵ -3p)=T4 = 0:623±0:056: We also tested a method using the Yang-Mills gradient flow. The preliminary results are consistent with those by the derivative method within the error.. |

34. | Yusuke Taniguchi, Shinji Ejiri, Kazuyuki Kanaya, Masakiyo Kitazawa, Hiroshi Suzuki, Takashi Umeda, Ryo Iwami, Naoki Wakabayashi, Temperature dependence of topological susceptibility using gradient flow, Proceedings of Science, Part F128557, 2016.01, We study temperature dependence of the topological susceptibility with the Nf = 2+1 flavors Wilson fermion. We have two major interests in this paper. One is a comparison of gluonic and fermionic definitions of the topological susceptibility. Two definitions are related by the chiral Ward-Takahashi identity but their coincidence is highly non-trivial for the Wilson fermion. By applying the gradient flow both for the gauge and quark fields we find a good agreement of these two measurements. The other is a verification of a prediction of the dilute instanton gas approximation at low temperature region T_{pc} < T < 1.5T_{pc}, for which we confirm the prediction that the topological susceptibility decays with power χτ ∝ (T/Tpc)^{-8} for three flavors QCD.. |

35. | Hiroshi Suzuki, Background field method in the gradient flow, Progress of Theoretical and Experimental Physics, 10.1093/ptep/ptv139, 2015, 10, 2015.10, In perturbative consideration of the Yang-Mills gradient flow, it is useful to introduce a gauge non-covariant term("gauge-fixing term") to the flow equation that gives rise to a Gaussian damping factor also for gauge degrees of freedom. In the present paper, we consider a modified formof the gauge-fixing termthat manifestly preserves covariance under the background gauge transformation. It is shown that our gauge-fixing term does not affect gauge-invariant quantities as does the conventional gauge-fixing term. The formulation thus allows a background gauge covariant perturbative expansion of the flow equation that provides, in particular, a very efficient computational method of expansion coefficients in the small flow time expansion. The formulation can be generalized to systems containing fermions.. |

36. | Hiroki Makino, Hiroshi Suzuki, Daisuke Takeda, Complex Langevin method applied to the 2D SU (2) Yang-Mills theory, Physical Review D - Particles, Fields, Gravitation and Cosmology, 10.1103/PhysRevD.92.085020, 92, 8, 2015.10, The complex Langevin method in conjunction with the gauge cooling is applied to the two-dimensional lattice SU(2) Yang-Mills theory that is analytically solvable. We obtain strong numerical evidence that at large Langevin time the expectation value of the plaquette variable converges, but to a wrong value when the complex phase of the gauge coupling is large.. |

37. | Background field method in the gradient flow The Yang--Mills gradient flow and its extension to the fermion field provide a very general method to obtain renormalized observables in gauge theory. The method is applicable also with non-perturbative regularization such as lattice. The gradient flow thus offers useful probes to study non-perturbative dynamics of gauge theory. In this work, aiming at possible simplification in perturbative calculations associated with the gradient flow, a modification of the gauge-fixed version of the flow equation, which preserves gauge covariance under the background gauge transformation, is proposed. This formulation allows for example a very quick one-loop calculation of the small flow time expansion of a composite operator that is relevant to the construction of a lattice energy--momentum tensor. Some details of the calculation, which have not been given elsewhere, are presented.. |

38. | Hiroki Makino, Hiroshi Suzuki, Daisuke Takeda, Complex Langevin method applied to the 2D SU(2) Yang-Mills theory, PHYSICAL REVIEW D, 10.1103/PhysRevD.92.085020, 92, 8, 2015.10, The complex Langevin method in conjunction with the gauge cooling is applied to the two-dimensional lattice SU(2) Yang-Mills theory that is analytically solvable. We obtain strong numerical evidence that at large Langevin time the expectation value of the plaquette variable converges, but to a wrong value when the complex phase of the gauge coupling is large.. |

39. | Masayuki Asakawa, Tetsuo Hatsuda, Etsuko Itou, Masakiyo Kitazawa, Hiroshi Suzuki, Erratum Thermodynamics of SU (3) gauge theory from gradient flow on the lattice (Physical Review D - Particles, Fields, Gravitation and Cosmology (2014) D 90 (011501)), Physical Review D - Particles, Fields, Gravitation and Cosmology, 10.1103/PhysRevD.92.059902, 92, 5, 2015.09. |

40. | Masayuki Asakawa, Tetsuo Hatsuda, Etsuko Itou, Masakiyo Kitazawa, Hiroshi Suzuki, Thermodynamics of SU(3) gauge theory from gradient flow on the lattice (vol 90, 011501, 2014), PHYSICAL REVIEW D, 10.1103/PhysRevD.92.059902, 92, 5, 2015.09. |

41. | Hiroshi Suzuki, Erratum Energy-momentum tensor from the Yang-Mills gradient flow (Progress of Theoretical and Experimental Physics (2013) 2013 (083B03)), Progress of Theoretical and Experimental Physics, 10.1093/ptep/ptv094, 2015, 7, 2015.07. |

42. | Hiroki Makino, Hiroshi Suzuki, Erratum Lattice energy-momentum tensor from the Yang-Mills gradient flow-inclusion of fermion fields (Progress of Theoretical and Experimental Physics (2014) 2014 (063B02)), Progress of Theoretical and Experimental Physics, 10.1093/ptep/ptv095, 2015, 7, 2015.07. |

43. | Tasuku Endo, Kenji Hieda, Daiki Miura, Hiroshi Suzuki, Universal formula for the flavor non-singlet axial-vector current from the gradient flow, Progress of Theoretical and Experimental Physics, 10.1093/ptep/ptv058, 2015, 5, 2015.05, By employing the gradient/Wilson flow, we derive a universal formula that expresses a correctly normalized flavor non-singlet axial-vector current of quarks. The formula is universal in the sense that it holds independently of regularization and especially holds with lattice regularization. It is also confirmed that, in the lowest non-trivial order of perturbation theory, the triangle diagram containing the formula and two flavor non-singlet vector currents possesses non-local structure that is compatible with the triangle anomaly.. |

44. | Masakiyo Kitazawa, Masayuki Asakawa, Tetsuo Hatsuda, Takumi Iritani, Etsuko Itou, Hiroshi Suzuki, Measurement of thermodynamics using gradient flow, Proceedings of Science, Part F130500, 2015.05, We analyze bulk thermodynamics and correlation functions of the energy-momentum tensor in pure Yang-Mills gauge theory using the energy-momentum tensor defined by the gradient flow and small flow time expansion. Our results on thermodynamic observables are consistent with those obtained by the conventional integral method. The analysis of the correlation function of total energy supports the energy conservation. It is also addressed that these analyses with gradient flow require less statistics compared with the previous methods. All these results suggest that the energy-momentum tensor can be successfully defined and observed on the lattice with moderate numerical costs with the gradient flow.. |

45. | Hiroshi Suzuki, Universal formula for the energy-momentum tensor via a flow equation in the Gross-Neveu model, Progress of Theoretical and Experimental Physics, 10.1093/ptep/ptv036, 2015, 4, 2015.04, For the fermion field in the two-dimensional Gross-Neveu model, we introduce a flow equation that allows a simple 1/N expansion. By employing the 1/N expansion, we examine the validity of a universal formula for the energy-momentum tensor which is based on the small flow-time expansion.We confirm that the formula reproduces a correct normalization and the conservation law of the energy-momentum tensor by computing the translation Ward-Takahashi relation in the leading non-trivial order in the 1/N expansion. Also, we confirmthat the expectation value at finite temperature correctly reproduces thermodynamic quantities. These observations support the validity of a similar construction of the energy-momentum tensor via the gradient/Wilson flow in lattice gauge theory.. |

46. | Kazuo Fujikawa, Hiroshi Suzuki, Bosonization in the path integral formulation, Physical Review D - Particles, Fields, Gravitation and Cosmology, 10.1103/PhysRevD.91.065010, 91, 6, 2015.03, We establish the direct d=2 on-shell bosonization ψL(x+)=eiξ(x+) and ψR†(x-)=eiξ(x-) in path integral formulation by deriving the off-shell relations ψL(x)ψR†(x)=exp[iξ(x)] and ψR(x)ψL†(x)=exp[-iξ(x)]. Similarly, the on-shell bosonization of the bosonic commuting spinor, φL(x+)=ie-iξ(x+)∂+e-iχ(x+), φR†(x-)=e-iξ(x-)-iχ(x-) and φR(x-)=ieiξ(x-)∂-e+iχ(x-), φL†(x+)=eiξ(x+)+iχ(x+), is established in path integral formulation by deriving the off-shell relations φL(x)φR†(x)=ie-iξ(x)∂+e-iχ(x) and φR(x)φL†(x)=ieiξ(x)∂-eiχ(x).. |

47. | Hiroshi Suzuki, Background field method in the gradient flow, Proceedings of Science, 14-18-July-2015, 2015.01, The Yang-Mills gradient flow and its extension to the fermion field provide a very general method to obtain renormalized observables in gauge theory. The method is applicable also with non- perturbative regularization such as lattice. The gradient flow thus offers useful probes to study non-perturbative dynamics of gauge theory. In this work, aiming at possible simplification in per-Turbative calculations associated with the gradient flow, a modification of the gauge-fixed version of the flow equation, which preserves gauge covariance under the background gauge transforma-Tion, is proposed. This formulation allows for example a very quick one-loop calculation of the small flow time expansion of a composite operator that is relevant to the construction of a lattice energy-momentum tensor. Some details of the calculation, which have not been given elsewhere, are presented.. |

48. | Hiroki Makino, Fumihiko Sugino, Hiroshi Suzuki, Large-N limit of the gradient flow in the 2D O(N) nonlinear sigma model, Progress of Theoretical and Experimental Physics, 10.1093/ptep/ptv044, 2015, 4, 2015.01, The gradient flow equation in the 2D O(N) nonlinear sigma model with lattice regularization is solved in the leading order of the 1/N expansion. By using this solution, we analytically compute the thermal expectation value of a lattice energy-momentum tensor defined through the gradient flow. The expectation value reproduces thermodynamic quantities obtained by the standard large-N method. This analysis confirms that the above lattice energy-momentum tensor restores the correct normalization automatically in the continuum limit, in a system with a nonperturbative mass gap.. |

49. | Masakiyo Kitazawa, Masayuki Asakawa, Tetsuo Hatsuda, Takumi Iritani, Etsuko Itou, Hiroshi Suzuki, Thermodynamics and reference scale of SU(3) gauge theory from gradient flow on fine lattices, Proceedings of Science, 14-18-July-2015, 2015.01, We study the parametrization of lattice spacing and thermodynamics of SU(3) gauge theory on the basis of the Yang-Mills gradient flow on fine lattices. The lattice spacing of the Wilson gauge action is determined over a wide range 6:3 ≤ b ≤ 7:5 with high accuracy. The measurements of the flow time and lattice spacing dependences of the expectation values of the energy-momentum tensor are performed on fine lattices.. |

50. | Hiroki Makino, Hiroshi Suzuki, Renormalizability of the gradient flow in the 2D O(N) non-linear sigma model, Progress of Theoretical and Experimental Physics, 10.1093/ptep/ptv028, 2015, 3, 2014.11, It is known that the gauge field and its composite operators evolved by the Yang-Mills gradient flow are ultraviolet (UV) finite without any multiplicative wave function renormalization. In this paper, we prove that the gradient flow in the 2D $O(N)$ non-linear sigma model possesses a similar property: The flowed $N$-vector field and its composite operators are UV finite without multiplicative wave function renormalization. Our proof in all orders of perturbation theory uses a $(2+1)$-dimensional field theoretical representation of the gradient flow, which possesses local gauge invariance without gauge field. As an application of the UV finiteness of the gradient flow, we construct the energy-momentum tensor in the lattice formulation of the $O(N)$ non-linear sigma model that automatically restores the correct normalization and the conservation law in the continuum limit.. |

51. | Masayuki Asakawa, Tetsuo Hatsuda, Etsuko Itou, Masakiyo Kitazawa, Hiroshi Suzuki, Thermodynamics of SU (3) gauge theory from gradient flow on the lattice, Physical Review D - Particles, Fields, Gravitation and Cosmology, 10.1103/PhysRevD.90.011501, 90, 1, 2014.07, A novel method to study the bulk thermodynamics in lattice gauge theory is proposed on the basis of the Yang-Mills gradient flow with a fictitious time t. The energy density and the pressure P of SU(3) gauge theory at fixed temperature are calculated directly on 323×(6,8,10) lattices from the thermal average of the well-defined energy-momentum tensor TμνR(x) obtained by the gradient flow. It is demonstrated that the continuum limit can be taken in a controlled manner from the t dependence of the flowed data.. |

52. | Masayuki Asakawa, Tetsuo Hatsuda, Etsuko Itou, Masakiyo Kitazawa, Hiroshi Suzuki, Thermodynamics of SU(3) gauge theory from gradient flow on the lattice, PHYSICAL REVIEW D, 10.1103/PhysRevD.90.011501, 90, 1, 2014.07, A novel method to study the bulk thermodynamics in lattice gauge theory is proposed on the basis of the Yang-Mills gradient flow with a fictitious time t. The energy density e and the pressure P of SU(3) gauge theory at fixed temperature are calculated directly on 32(3) x (6, 8, 10) lattices from the thermal average of the well-defined energy-momentum tensor T-mu nu(R)(x) obtained by the gradient flow. It is demonstrated that the continuum limit can be taken in a controlled manner from the t dependence of the flowed data.. |

53. | Hiroki Makino, Hiroshi Suzuki, Lattice energy-momentum tensor from the yang. Mills gradient flow-inclusion of fermion fields, Progress of Theoretical and Experimental Physics, 10.1093/ptep/ptu070, 2014, 6, 2014.01, Local products of fields deformed by the so-called Yang-Mills gradient flow become renormalized composite operators. This fact has been utilized to construct a correctly normalized conserved energy-momentum tensor in the lattice formulation of the pure Yang-Mills theory. In the present paper, this construction is further generalized for vector-like gauge theories containing fermions.. |

54. | Michael G. Endres, Tsunehide Kuroki, Fumihiko Sugino, Hiroshi Suzuki, SUSY breaking by nonperturbative dynamics in a matrix model for 2D type IIA superstrings, Nuclear Physics B, 10.1016/j.nuclphysb.2013.09.005, 876, 3, 758-793, 2013.11, We explicitly compute nonperturbative effects in a supersymmetric double-well matrix model corresponding to two-dimensional type IIA superstring theory on a nontrivial Ramond-Ramond background. We analytically determine the full one-instanton contribution to the free energy and one-point function, including all perturbative fluctuations around the one-instanton background. The leading order two-instanton contribution is determined as well. We see that supersymmetry is spontaneously broken by instantons, and that the breaking persists after taking a double scaling limit which realizes the type IIA theory from the matrix model. The result implies that spontaneous supersymmetry breaking occurs by nonperturbative dynamics in the target space of the IIA theory. Furthermore, we numerically determine the full nonperturbative effects by recursive evaluation of orthogonal polynomials. The free energy of the matrix model appears well-defined and finite even in the strongly coupled limit of the corresponding type IIA theory. The result might suggest a weakly coupled theory appearing as an S-dual to the two-dimensional type IIA superstring theory.. |

55. | Hiroshi Suzuki, Energy-momentum tensor from the yang-mills gradient flow, Progress of Theoretical and Experimental Physics, 10.1093/ptep/ptt059, 2013, 8, 2013.08, The product of gauge fields generated by the Yang-Mills gradient flow for positive flow times does not exhibit the coincidence-point singularity and a local product is thus independent of the regularization. Such a local product can furthermore be expanded by renormalized local operators at zero flow time with finite coefficients that are governed by renormalization group equations. Using these facts, we derive a formula that relates the small flow-time behavior of certain gauge-invariant local products and the correctly-normalized conserved energy-momentum tensor in the Yang-Mills theory. Our formula provides a possible method to compute the correlation functions of a well-defined energy-momentum tensor by using lattice regularization and Monte Carlo simulation.. |

56. | Hiroshi Suzuki, Ferrara-Zumino supermultiplet and the energy-momentum tensor in the lattice formulation of 4D N=1 SYM, Nuclear Physics B, 10.1016/j.nuclphysb.2012.11.023, 868, 2, 459-475, 2013.03, It is well-known that Noether currents in the classical four-dimensional N=1 supersymmetric Yang-Mills theory (4D N=1 SYM), i.e., the U(1)_{A} current, the supersymmetry (SUSY) current and the energy-momentum tensor, form a multiplet under SUSY, called the Ferrara-Zumino supermultiplet. Inspired by this structure, we define the energy-momentum tensor in the lattice formulation of 4D N=1 SYM by a renormalized super transformation of a lattice SUSY current. By using a renormalized SUSY Ward-Takahashi relation, the energy-momentum tensor so constructed is shown to be conserved in the quantum continuum limit. Our construction of the energy-momentum tensor is very explicit and usable in non-perturbative numerical simulations.. |

57. | Hiroshi Suzuki, Remark on the energy-momentum tensor in the lattice formulation of 4D N=1 SYM, Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, 10.1016/j.physletb.2013.01.028, 719, 4-5, 435-439, 2013.02, In a recent paper, Suzuki (2013) [1], we presented a possible definition of the energy-momentum tensor in the lattice formulation of the four-dimensional N=1 supersymmetric Yang-Mills theory, that is conserved in the quantum continuum limit. In the present Letter, we propose a quite similar but somewhat different definition of the energy-momentum tensor (that is also conserved in the continuum limit) which is superior in several aspects: In the continuum limit, the origin of the energy automatically becomes consistent with the supersymmetry and the number of renormalization constants that require a (non-perturbative) determination is reduced to two from four, the number of renormalization constants appearing in the construction in Suzuki (2013) [1].. |

58. | Hiroshi Suzuki, Supersymmetry, chiral symmetry and the generalized BRS transformation in lattice formulations of 4D N=1 SYM, Nuclear Physics B, 10.1016/j.nuclphysb.2012.04.008, 861, 3, 290-320, 2012.08, In the context of the lattice regularization of the four-dimensional N=1 supersymmetric Yang-Mills theory (4D N=1 SYM), we formulate a generalized BRS transformation that treats the gauge, supersymmetry (SUSY), translation and axial U(1) (U(1) _{A}) transformations in a unified way. A resultant Slavnov-Taylor identity or the Zinn-Justin equation gives rise to a strong constraint on the quantum continuum limit of symmetry breaking terms with the lattice regularization. By analyzing the implications of the constraint on operator-mixing coefficients in the SUSY and the U(1) _{A} Ward-Takahashi (WT) identities, we prove to all orders of perturbation theory in the continuum limit that, (i) the chiral symmetric limit implies the supersymmetric limit and, (ii) a three-fermion operator that might potentially give rise to an exotic breaking of the SUSY WT identity does not emerge. In previous literature, only a naive or incomplete treatment on these points can be found. Our results provide a solid theoretical basis for lattice formulations of the 4D N=1 SYM.. |

59. | Syo Kamata, Hiroshi Suzuki, Numerical simulation of the N=(2,2) Landau-Ginzburg model, Nuclear Physics B, 10.1016/j.nuclphysb.2011.09.007, 854, 3, 552-574, 2012.01, The two-dimensional N=(2,2) Wess-Zumino (WZ) model with a cubic superpotential is numerically studied with a momentum-cutoff regularization that preserves supersymmetry. A numerical algorithm based on the Nicolai map is employed and the resulting configurations have no autocorrelation. This system is believed to flow to an N=(2,2) superconformal field theory (SCFT) in the infrared (IR), the A2 model. From a finite-size scaling analysis of the susceptibility of the scalar field in the WZ model, we determine 1-h-h̄=0.616(25)(13) for the conformal dimensions h and h̄, while 1-h-h̄=0.666. . for the A2 model. We also measure the central charge in the IR region from a correlation function between conserved supercurrents and obtain c=1.09(14)(31) (c=1 for the A2 model). These results are consistent with the conjectured emergence of the A2 model, and at the same time demonstrate that numerical studies can be complementary to analytical investigations for this two-dimensional supersymmetric field theory.. |

60. | Daisuke Kadoh, Hiroshi Suzuki, Supersymmetry restoration in lattice formulations of 2D N=(2,2) WZ model based on the Nicolai map, Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, 10.1016/j.physletb.2010.12.012, 696, 1-2, 163-166, 2011.01, For lattice formulations of the two-dimensional N=(2,2) Wess-Zumino (2D N=(2,2) WZ) model on the basis of the Nicolai map, we show that supersymmetry (SUSY) and other symmetries are restored in the continuum limit without fine tuning, to all orders in perturbation theory. This provides a theoretical basis for use of these lattice formulations for computation of correlation functions.. |

61. | Daisuke Kadoh, Hiroshi Suzuki, Supersymmetric nonperturbative formulation of the WZ model in lower dimensions, Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, 10.1016/j.physletb.2010.01.022, 684, 2-3, 167-172, 2010.02, A nonperturbative formulation of the Wess-Zumino (WZ) model in two and three dimensions is proposed on the basis of momentum-modes truncation. The formulation manifestly preserves full supersymmetry as well as the translational invariance and all global symmetries, while it is shown to be consistent with the expected locality to all orders of perturbation theory. For the two-dimensional WZ model, a well-defined Nicolai map in the formulation provides an interesting algorithm for Monte Carlo simulations.. |

62. | Daisuke Kadoh, Hiroshi Suzuki, SUSY WT identity in a lattice formulation of 2D N = (2, 2) SYM, Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, 10.1016/j.physletb.2009.11.028, 682, 4-5, 466-471, 2010.01, We address some issues relating to a supersymmetric (SUSY) Ward-Takahashi (WT) identity in Sugino's lattice formulation of two-dimensional (2D) N = (2, 2) SU (k) supersymmetric Yang-Mills theory (SYM). A perturbative argument shows that the SUSY WT identity in the continuum theory is reproduced in the continuum limit without any operator renormalization/mixing and tuning of lattice parameters. As application of the lattice SUSY WT identity, we show that a prescription for the Hamiltonian density in this lattice formulation, proposed by Kanamori, Sugino and Suzuki, is justified also from a perspective of an operator algebra among correctly-normalized supercurrents. We explicitly confirm the SUSY WT identity in the continuum limit to the first nontrivial order in a semi-perturbative expansion.. |

63. | Daisuke Kadoh, Fumihiko Sugino, Hiroshi Suzuki, Lattice formulation of 2D N = (2, 2) SQCD based on the B model twist, Nuclear Physics B, 10.1016/j.nuclphysb.2009.05.012, 820, 1-2, 99-115, 2009.10, We present a simple lattice formulation of two-dimensional N = (2, 2)U (k) supersymmetric QCD (SQCD) with N matter multiplets in the fundamental representation. The construction uses compact gauge link variables and exactly preserves one linear combination of supercharges on the two-dimensional regular lattice. Artificial saddle points in the weak coupling limit and the species doubling are evaded without imposing the admissibility. A perturbative power-counting argument indicates that the target supersymmetric theory is realized in the continuum limit without any fine tuning.. |

64. | Issaku Kanamori, Hiroshi Suzuki, Restoration of supersymmetry on the lattice Two-dimensional N = (2, 2) supersymmetric Yang-Mills theory, Nuclear Physics B, 10.1016/j.nuclphysb.2008.11.021, 811, 3, 420-437, 2009.04, By numerically investigating the conservation law of the supercurrent, we confirm the restoration of supersymmetry in Sugino's lattice formulation of the two-dimensional N = (2, 2) supersymmetric SU (2) Yang-Mills theory with a scalar mass term. Subtlety in the case without the scalar mass term, that appears to ruin perturbative power counting, is also pointed out.. |

65. | Issaku Kanamori, Hiroshi Suzuki, Some physics of the two-dimensional N = (2, 2) supersymmetric Yang-Mills theory Lattice Monte Carlo study, Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, 10.1016/j.physletb.2009.01.039, 672, 3, 307-311, 2009.02, We illustrate some physical application of a lattice formulation of the two-dimensional N = (2, 2) supersymmetric SU (2) Yang-Mills theory with a (small) supersymmetry breaking scalar mass. Two aspects, power-like behavior of certain correlation functions (which implies the absence of the mass gap) and the static potential V (R) between probe charges in the fundamental representation, are considered. For the latter, for R ≲ 1 / g, we observe a linear confining potential with a finite string tension. This confining behavior appears distinct from a theoretical conjecture that a probe charge in the fundamental representation is screened in two-dimensional gauge theory with an adjoint massless fermion, although the static potential for R ≳ 1 / g has to be systematically explored to conclude real asymptotic behavior in large distance.. |

66. | Issaku Kanamori, Hiroshi Suzuki, Fumihiko Sugino, Euclidean lattice simulation for dynamical supersymmetry breaking, Physical Review D - Particles, Fields, Gravitation and Cosmology, 10.1103/PhysRevD.77.091502, 77, 9, 2008.05, The global supersymmetry is spontaneously broken if and only if the ground-state energy is strictly positive. We propose to use this fact to observe the spontaneous supersymmetry breaking in Euclidean lattice simulations. For lattice formulations that possess a manifest fermionic symmetry, there exists a natural choice of a Hamiltonian operator that is consistent with a topological property of the Witten index. We confirm validity of our idea in models of the supersymmetric quantum mechanics. We then examine a possibility of a dynamical supersymmetry breaking in the two-dimensional N=(2,2) super Yang-Mills theory with the gauge group SU(2), for which the Witten index is unknown. Differently from a recent conjectural claim, our numerical result tempts us to conclude that supersymmetry is not spontaneously broken in this system.. |

67. | Issaku Kanamori, Fumihiko Sugino, Hiroshi Suzuki, Observing dynamical supersymmetry breaking with euclidean lattice simulations, Progress of Theoretical Physics, 10.1143/PTP.119.797, 119, 5, 797-827, 2008.05, A strict positivity of the ground-state energy is a necessary and sufficient condition for spontaneous supersymmetry breaking. This ground-state energy may be directly determined from the expectation value of the Hamiltonian in the functional integral, defined with an antiperiodic temporal boundary condition for all fermionic variables. We propose to use this fact to observe the dynamical spontaneous supersymmetry breaking in Euclidean lattice simulations. If a lattice formulation possesses a manifestly preserved fermionic symmetry, there exists a natural choice of a Hamiltonian operator that is consistent with a topological nature of the Witten index. We numerically confirm the validity of our idea in models of supersymmetric quantum mechanics. We further examine the possibility of dynamical supersymmetry breaking in the two-dimensional N = (2, 2) super Yang-Mills theory with the gauge group SU(2), for which the Witten index is unknown. Although statistical errors are still large, we do not observe positive ground-state energy, at least within one standard deviation. This prompts us to draw a different conclusion from a recent conjectural claim that supersymmetry is dynamically broken in this system.. |

68. | Yoshio Kikukawa, Hiroshi Suzuki, Four-dimensional lattice chiral gauge theories with anomalous fermion content, Journal of High Energy Physics, 10.1088/1126-6708/2007/10/018, 2007, 10, 2007.10, In continuum field theory, it has been discussed that chiral gauge theories with Weyl fermions in anomalous gauge representations (anomalous gauge theories) can consistently be quantized, provided that some of gauge bosons are permitted to acquire mass. Such theories in four dimensions are inevitablly non-renormalizable and must be regarded as a low-energy effective theory with a finite ultraviolet (UV) cutoff. In this paper, we present a lattice framework which enables one to study such theories in a non-perturbative level. By introducing bare mass terms of gauge bosons that impose ''smoothness'' on the link field, we explicitly construct a consistent fermion integration measure in a lattice formulation based on the Ginsparg-Wilson (GW) relation. This framework may be used to determine in a non-perturbative level an upper bound on the UV cutoff in low-energy effective theories with anomalous fermion content. By further introducing the Stückelberg or Wess-Zumino (WZ) scalar field, this framework provides also a lattice definition of a non-linear sigma model with the Wess-Zumino-Witten (WZW) term.. |

69. | Yoshio Kikukawa, Hiroshi Suzuki, Four-dimensional lattice chiral gauge theories with anomalous fermion content, JOURNAL OF HIGH ENERGY PHYSICS, 10, 2007.10, In continuum field theory, it has been discussed that chiral gauge theories with Weyl fermions in anomalous gauge representations (anomalous gauge theories) can consistently be quantized, provided that some of gauge bosons are permitted to acquire mass. Such theories in four dimensions are inevitablly non-renormalizable and must be regarded as a low-energy effective theory with a finite ultraviolet (UV) cutoff. In this paper, we present a lattice framework which enables one to study such theories in a non-perturbative level. By introducing bare mass terms of gauge bosons that impose "smoothness" on the link field, we explicitly construct a consistent fermion integration measure in a lattice formulation based on the Ginsparg-Wilson (GW) relation. This framework may be used to determine in a non-perturbative level an upper bound on the UV cutoff in low-energy effective theories with anomalous fermion content. By further introducing the Stiiekelberg or Wess-Zumino (WZ) scalar field, this framework provides also a lattice definition of a non-linear sigma model with the Wess-Zumino-Witten (WZW) term.. |

70. | Hiroshi Suzuki, Two-dimensional N ≤ (2,2) super Yang-Mills theory on computer, Journal of High Energy Physics, 10.1088/1126-6708/2007/09/052, 2007, 9, 2007.09, We carry out preliminary numerical study of Sugino's lattice formulation [1, 2] of the two-dimensional ≤ (2,2) super Yang-Mills theory (2d ≤ (2,2) SYM) with the gauge group SU(2). The effect of dynamical fermions is included by re-weighting a quenched ensemble by the pfaffian factor. It appears that the complex phase of the pfaffian due to lattice artifacts and flat directions of the classical potential are not problematic in Monte Carlo simulation. Various one-point supersymmetric Ward-Takahashi (WT) identities are examined for lattice spacings up to a ≤ 0.5/g with the fixed physical lattice size L ≤ 4.0/g, where g denotes the gauge coupling constant in two dimensions. WT identities implied by an exact fermionic symmetry of the formulation are confirmed in fair accuracy and, for most of these identities, the quantum effect of dynamical fermions is clearly observed. For WT identities expected only in the continuum limit, the results seem to be consistent with the behavior expected from supersymmetry, although we do not see clear distintion from the quenched simulation. We measure also the expectation values of renormalized gauge-invariant bi-linear operators of scalar fields.. |

71. | Numerical results of two-dimensional N=(2,2) super Yang-Mills theory We report the results of a numerical simulation of a lattice formulation of the two-dimensional N=(2,2) super Yang-Mills theory proposed by Suzuki and Taniguchi. We measure the 1-point functions and 2-point functions. The scenario is that only tuning of the scalar mass to a specific value gives a supersymmetric continuum limit. Our results are consistent with this scenario although conclusive results on the restoration of supersymmetry have not been obtained.. |

72. | Hidenori Fukaya, Issaku Kanamori, Hiroshi Suzuki, Tomohisa Takimi, Numerical results of two-dimensional N = (2,2) super Yang-Mills theory, 25th International Symposium on Lattice Field Theory, LATTICE 2007
Proceedings of Science, 42, 2007.01, We report the results of a numerical simulation of a lattice formulation of the two-dimensional N = (2,2) super Yang-Mills theory proposed by Suzuki and Taniguchi [1]. We measure the 1-point functions and 2-point functions. The scenario is that only tuning of the scalar mass to a specific value gives a supersymmetric continuum limit. Our results are consistent with this scenario although conclusive results on the restoration of supersymmetry have not been obtained.. |

73. | Hidenori Fukaya, Masashi Hayakawa, Issaku Kanamori, Hiroshi Suzuki, Tomohisa Takimi, Note on massless bosonic states in two-dimensional field theories, Progress of Theoretical Physics, 10.1143/PTP.116.1117, 116, 6, 1117-1129, 2006.12, In a wide class of G_{L} × G_{R} invariant two-dimensional super-renormalizable field theories, the parity-odd part of the two-point function of global currents is completely determined by a fermion one-loop diagram. For any non-trivial fermion content, the two-point function possesses a massless pole which corresponds to massless bosonic physical states. As an application, we show that two-dimensional N= (2,2) supersymmetric gauge theory without a superpotential possesses U (1)_{L} × U(1) _{R} symmetry and contains one massless bosonic state per fixed spatial momentum. The N = (4,4) supersymmetric pure Yang-Mills theory possesses SU(2)_{L} × SU(2)_{R} symmetry, and there exist at least three massless bosonic states.. |

74. | Overlap Fermion in External Gravity On a lattice, we construct an overlap Dirac operator which describes the propagation of a Dirac fermion in external gravity. The local Lorentz symmetry is manifestly realized as a lattice gauge symmetry, while the general coordinate invariance is expected to be restored only in the continuum limit. The lattice index density in the presence of a gravitational field is calculated.. |

75. | Y. Hatsugai, T. Fukui, Hiroshi Suzuki, Topological description of (spin) Hall conductances on Brillouin zone lattices quantum phase transitions and topological changes, Physica E: Low-Dimensional Systems and Nanostructures, 10.1016/j.physe.2006.03.141, 34, 1-2, 336-339, 2006.08, It is widely accepted that topological quantities are useful to describe quantum liquids in low dimensions. The (spin) Hall conductances are typical examples. They are expressed by the Chern numbers, which are topological invariants given by the Berry connections of the ground states. We present a topological description for the (spin) Hall conductances on a discretized Brillouin zone. At the same time, it is quite efficient in practical numerical calculations for concrete models. We demonstrate its validity in a model with quantum phase transitions. Topological changes supplemented with the transition is also described in the present lattice formulation.. |

76. | Masashi Hayakawa, Hiroto So, Hiroshi Suzuki, Overlap lattice fermion in a gravitational field, Progress of Theoretical Physics, 10.1143/PTP.116.197, 116, 1, 197-215, 2006.07, We construct a lattice Dirac operator of overlap type that describes the propagation of a Dirac fermion in an external gravitational field. The local Lorentz symmetry is manifestly realized as a lattice gauge symmetry, while it is believed that the general coordinate invariance is restored only in the continuum limit. Our doubler-free Dirac operator satisfies the conventional Ginsparg-Wilson relation and possesses γ_{5} hermiticity with respect to the inner product, which is suggested by the general coordinate invariance. The lattice index theorem in the presence of a gravitational field holds, and the classical continuum limit of the index density reproduces the Dirac genus. Reduction to a single Majorana fermion is possible for 8k + 2 and 8k + 4 dimensions, but not for 8k dimensions, which is consistent with the existence of the global gravitational/gauge anomalies in 8k dimensions. Other Lorentz representations, such as the spinor-vector and the bi-spinor representations, can also be treated. Matter fields with a definite chirality (with respect to the lattice-modified chiral matrix) are briefly considered.. |

77. | Masashi Hayakawa, Hiroshi Suzuki, Gauge anomaly associated with the Majorana fermion in 8k + 1 dimensions, Progress of Theoretical Physics, 10.1143/PTP.115.1129, 115, 6, 1129-1136, 2006.06, Using an elementary method, we show that an odd number of Majorana fermions in 8k + 1 dimensions suffer from a gauge anomaly that is analogous to the Witten global gauge anomaly. This anomaly cannot be removed without sacrificing the perturbative gauge invariance. Our construction of higher-dimensional examples (k ≥ 1) makes use of the SO(8) instanton on S^{8}.. |

78. | Hiroto So, Hiroshi Suzuki, Zero-dimensional analogue of the global gauge anomaly, Progress of Theoretical Physics, 10.1143/PTP.115.467, 115, 2, 467-471, 2006.02, A zero-dimensional analogue of Witten's global gauge anomaly is considered. For example, a zero-dimensional reduction of the two-dimensional SO(2N) Yang-Mills theory with a single Majorana-Weyl fermion in the fundamental representation suffers from this anomaly. Another example is a zero-dimensional reduction of two- and three-dimensional SU(2N_{C}) Yang-Mills theories which couple to a single Majorana fermion in the adjoint representation. In this case, any expectation value is either indeterminate or infinite.. |

79. | Hiroto So, Masashi Hayakawa, Hiroshi Suzuki, Overlap fermion in external gravity, 24th International Symposium on Lattice Field Theory, LATTICE 2006
Proceedings of Science, 32, 2006.01, On a lattice, we construct an overlap Dirac operator which describes the propagation of a Dirac fermion in external gravity. The local Lorentz symmetry is manifestly realized as a lattice gauge symmetry, while the general coordinate invariance is expected to be restored only in the continuum limit. The lattice index density in the presence of a gravitational field is calculated.. |

80. | Hiroshi Suzuki, Yusuke Taniguchi, Two dimensional N ≤(2,2) super Yang-Mills theory on the lattice via dimensional reduction, Journal of High Energy Physics, 10.1088/1126-6708/2005/10/082, 10, 1987-2008, 2005.10, The N ≤ (2,2) extended super Yang-Mills theory in 2 dimensions is formulated on the lattice as a dimensional reduction of a 4 dimensional lattice gauge theory. We use the plaquette action for a bosonic sector and the Wilson- or the overlap-Dirac operator for a fermion sector. The fermion determinant is real and, moreover, when the overlap-Dirac operator is used, semi-positive definite. The flat directions in the target theory become compact and present no subtlety for a numerical integration along these directions. Any exact supersymmetry does not exist in our lattice formulation; nevertheless we argue that one-loop calculable and finite mass counter terms ensure a supersymmetric continuum limit to all orders of perturbation theory.. |

81. | Takahiro Fukui, Yasuhiro Hatsugai, Hiroshi Suzuki, Chern numbers in discretized Brillouin zone Efficient method of computing (spin) Hall conductances, journal of the physical society of japan, 10.1143/JPSJ.74.1674, 74, 6, 1674-1677, 2005.06, We present a manifestly gauge-invariant description of Chern numbers associated with the Berry connection defined on a discretized Brillouin zone. It provides an efficient method of computing (spin) Hall conductances without specifying gauge-fixing conditions. We demonstrate that it correctly reproduces quantized Hall conductances even on a coarsely discretized Brillouin zone. A gauge-dependent integer-valued field, which plays a key role in the formulation, is evaluated in several gauges. An extension to the non-Abelian Berry connection is also given.. |

82. | Yoshio Kikukawa, Hiroshi Suzuki, A local formulation of lattice Wess-Zumino model with exact U(l) _{R} symmetry, Journal of High Energy Physics, 2, 243-273, 2005.02, A lattice Wess-Zumino model is formulated on the basis of Ginsparg-Wilson fermions. In perturbation theory, our formulation is equivalent to the formulation by Fujikawa and Ishibashi and by Fujikawa. Our formulation is, however, free from a singular nature of the latter formulation due to an additional auxiliary chiral supermultiplet on a lattice. The model posssesses an exact U(1)_{R} symmetry as a supersymmetric counterpart of the Lüscher lattice chiral U(1) symmetry. A restration of the supersymmetric Ward-Takahashi identity in the continuum limit is analyzed in renormalized perturbation theory. In the one-loop level, a supersymmetric continuum limit is ensured by suitably adjusting a coefficient of a single local term F̃*F̃. The non-renormalization theorem holds to this order of perturbation theory. In higher orders, on the other hand, coefficents of local terms with dimension ≤ 4 that are consistent with the U(1)_{R} symmetry have to be adjusted for a supersymmetric continuum limit. The origin of this complexicity in higher-order loops is clarified on the basis of the Reisz power counting theorem. Therefore, from a view point of supersymmetry, the present formulation is not quite better than a lattice Wess-Zumino model formulated by using Wilson fermions, although a number of coefficients which require adjustment is much less due to the exact U(1)_{R} symmetry. We also comment on an exact non-linear fermionic symmetry which corresponds to the one studied by Bonini and Feo; an existence of this exact symmetry itself does not imply a restoration of supersymmetry in the continuum limit without any adjustment of parameters.. |

83. | Kosuke Matsui, Hiroshi Suzuki, Anomalous gauge theories revisited, Journal of High Energy Physics, 1, 1173-1190, 2005.01, A possible formulation of chiral gauge theories with an anomalous fermion content is re-examined in light of the lattice framework based on the Ginsparg-Wilson relation. It is shown that the fermion sector of a wide class of anomalous non-abelian theories cannot consistently be formulated within this lattice framework. In particular, in 4 dimension, all anomalous non-abelian theories are included in this class. Anomalous abelian chiral gauge theories cannot be formulated with compact U(1) link variables, while a non-compact formulation is possible at least for the vacuum sector in the space of lattice gauge fields. Our conclusion is not applied to effective low-energy theories with an anomalous fermion content which are obtained from an underlying anomaly-free theory by sending the mass of some of fermions to infinity. For theories with an anomalous fermion content in which the anomaly is cancelled by the Green-Schwarz mechanism, a possibility of a consistent lattice formulation is not clear.. |

84. | A local formulation of lattice Wess-Zumino model with exact $U(1)_R$ symmetry A lattice Wess-Zumino model is formulated on the basis of Ginsparg-Wilson fermions. In perturbation theory, our formulation is equivalent to the formulation by Fujikawa and Ishibashi and by Fujikawa. Our formulation is, however, free from a singular nature of the latter formulation due to an additional auxiliary chiral supermultiplet on a lattice. The model posssesses an exact $U(1)_R$ symmetry as a supersymmetric counterpart of the L"uscher lattice chiral $U(1)$ symmetry. A restration of the supersymmetric Ward-Takahashi identity in the continuum limit is analyzed in renormalized perturbation theory. In the one-loop level, a supersymmetric continuum limit is ensured by suitably adjusting a coefficient of a single local term $ ilde F^* ilde F$. The non-renormalization theorem holds to this order of perturbation theory. In higher orders, on the other hand, coefficents of local terms with dimension $leq4$ that are consistent with the $U(1)_R$ symmetry have to be adjusted for a supersymmetric continuum limit. The origin of this complexicity in higher-order loops is clarified on the basis of the Reisz power counting theorem. Therefore, from a view point of supersymmetry, the present formulation is not quite better than a lattice Wess-Zumino model formulated by using Wilson fermions, although a number of coefficients which require adjustment is much less due to the exact $U(1)_R$ symmetry. We also comment on an exact non-linear fermionic symmetry which corresponds to the one studied by Bonini and Feo; an existence of this exact symmetry itself does not imply a restoration of supersymmetry in the continuum limit without any adjustment of parameters.. |

85. | Anomalous gauge theories revisited A possible formulation of chiral gauge theories with an anomalous fermion content is re-examined in light of the lattice framework based on the Ginsparg-Wilson relation. It is shown that the fermion sector of a wide class of anomalous non-abelian theories cannot consistently be formulated within this lattice framework. In particular, in 4 dimension, {it all} anomalous non-abelian theories are included in this class. Anomalous abelian chiral gauge theories cannot be formulated with compact $U(1)$ link variables, while a non-compact formulation is possible at least for the vacuum sector in the space of lattice gauge fields. Our conclusion is not applied to effective low-energy theories with an anomalous fermion content which are obtained from an underlying anomaly-free theory by sending the mass of some of fermions to infinity. For theories with an anomalous fermion content in which the anomaly is cancelled by the Green-Schwarz mechanism, a possibility of a consistent lattice formulation is not clear.. |

86. | Hiroshi Suzuki, A no-go theorem for the Majorana fermion on a lattice, Progress of Theoretical Physics, 10.1143/PTP.112.855, 112, 5, 855-861, 2004.11, A variant of the Nielsen-Ninomiya no-go theorem is formulated. This theorem states that, under several assumptions, it is impossible to write down a doubler-free Euclidean lattice action of a single Majorana fermion in 8k and 8k + 1 dimensions.. |

87. | Teruaki Inagaki, Hiroshi Suzuki, Majorana and Majorana-Weyl fermions in lattice gauge theory, Journal of High Energy Physics, 8, 7, 901-930, 2004.07, In various dimensional euclidean lattice gauge theories, we examine a compatibility of the Majorana decomposition and the charge conjugation property of lattice Dirac operators. In 8n and 1 + 8n dimensions, we find a difficulty to decompose a classical lattice action of the Dirac fermion into a system of the Majorana fermion and thus to obtain a factrized form of the Dirac determinant. Similarly, in 2 + 8n dimensions, there is a difficulty to decompose a classical lattice action of the Weyl fermion into a system of the Majorana-Weyl fermion and thus to obtain a factrized form of the Weyl determinant. Prescriptions based on the overlap formalism do not remove these difficulties. We argue that these difficulties are reflections of the global gauge anomaly associated to the real Weyl fermion in 8n dimensions. For this reason (besides other well-known reasons), a lattice formulation of the N = 1 super Yang-Mills theory in these dimensions is expected to be extremely difficult to find.. |

88. | Majorana and Majorana-Weyl fermions in lattice gauge theory In various dimensional Euclidean lattice gauge theories, we examine a compatibility of the Majorana decomposition and the charge conjugation property of lattice Dirac operators. In $8n$ and $1+8n$ dimensions, we find a difficulty to decompose a classical lattice action of the Dirac fermion into a system of the Majorana fermion and thus to obtain a factorized form of the Dirac determinant. Similarly, in $2+8n$ dimensions, there is a difficulty to decompose a classical lattice action of the Weyl fermion into a system of the Majorana--Weyl fermion and thus to obtain a factrized form of the Weyl determinant. Prescriptions based on the overlap formalism do not remove these difficulties. We argue that these difficulties are reflections of the global gauge anomaly associated to the real Weyl fermion in $8n$ dimensions. For this reason (besides other well-known reasons), a lattice formulation of the N=1 super Yang--Mills theory in these dimensions is expected to be extremely difficult to find.. |

89. | Kazuo Fujikawa, Hiroshi Suzuki, Anomalies, local counter terms and bosonization, Physics Reports, 10.1016/j.physrep.2004.05.002, 398, 4-6, 221-243, 2004.01, We re-examine the issue of local counter terms in the analysis of quantum anomalies. We analyze two-dimensional theories and show that the notion of local counter terms need to be carefully defined depending on the physics contents such as whether one is analyzing gauge theory or bosonization. It is shown that a part of the Jacobian, which is apparently spurious and eliminated by a local counter term corresponding to the mass term of the gauge field in gauge theory, cannot be removed by a local counter term and plays a central role by giving the kinetic term of the bosonized field in the context of path integral bosonization.. |

90. | Teruaki Inagaki, Yoshio Kikukawa, Hiroshi Suzuki, Axial anomaly in the reduced model Higher representations, Nuclear Physics B - Proceedings Supplements, 10.1016/S0920-5632(03)02623-9, 129-130, 504-506, 2004.01, The topological charge in the U(N) vector-like reduced model can be defined by rising the overlap Dirac operator. We obtain its large N limit for a fermion in a general gauge-group representation under a certain restriction of gauge field configurations which is termed U(1) embedding.. |

91. | Kazuo Fujikawa, Hiroshi Suzuki, Domain wall fermion and CP symmetry breaking, Physical Review D, 10.1103/PhysRevD.67.034506, 67, 3, 2003.12, We examine the CP properties of chiral gauge theory defined by a formulation of the domain wall fermion, where the light field variables q and q̄ together with Pauli-Villars fields Q and Q̄ are utilized. It is shown that this domain wall representation in the infinite flavor limit N=∝ is valid only in the topologically trivial sector, and that the conflict among lattice chiral symmetry, strict locality and CP symmetry still persists for finite lattice spacing a. The CP transformation generally sends one representation of lattice chiral gauge theory into another representation of lattice chiral gauge theory, resulting in the inevitable change of propagators. A modified form of lattice CP transformation motivated by the domain wall fermion, which keeps the chiral action in terms of the Ginsparg-Wilson fermion invariant, is analyzed in detail; this provides an alternative way to understand the breaking of CP symmetry at least in the topologically trivial sector. We note that the conflict with CP symmetry could be regarded as a topological obstruction. We also discuss the issues related to the definition of Majorana fermions in connection with the supersymmetric Wess-Zumino model on the lattice.. |

92. | Takanori Fujiwara, Hiroshi Suzuki, Kosuke Matsui, Masaru Yamamoto, Wess-Zumino-Witten term on the lattice, Journal of High Energy Physics, 7, 9, 317-342, 2003.09, We construct the Wess-Zumino-Witten (WZW) term in lattice gauge theory by using a Dirac operator which obeys the Ginsparg-Wilson relation. Topological properties of the WZW term known in the continuum are reproduced on the lattice as a consequence of a non-trivial topological structure of the space of admissible lattice gauge fields. In the course of this analysis, we observe that the gauge anomaly generally implies that there is no basis of a Weyl fermion which leads to a single-valued expectation value in the fermion sector. The lattice Witten term, which carries information of a gauge path along which the gauge anomaly is integrated, is separated from the WZW term and the multivaluedness of the Witten term is shown to be related to the homotopy group π_{2n+1}(G). We also discuss the global SU(2) anomaly on the basis of the WZW term.. |

93. | Wess-Zumino-Witten term on the lattice We construct the Wess-Zumino-Witten (WZW) term in lattice gauge theory by using a Dirac operator which obeys the Ginsparg-Wilson relation. Topological properties of the WZW term known in the continuum are reproduced on the lattice as a consequence of a non-trivial topological structure of the space of admissible lattice gauge fields. In the course of this analysis, we observe that the gauge anomaly generally implies that there is no basis of a Weyl fermion which leads to a single-valued expectation value in the fermion sector. The lattice Witten term, which carries information of a gauge path along which the gauge anomaly is integrated, is separated from the WZW term and the multivaluedness of the Witten term is shown to be related to the homotopy group $pi_{2n+1}(G)$. We also discuss the global $SU(2)$ anomaly on the basis of the WZW term.. |

94. | Teruaki Inagaki, Yoshio Kikukawa, Hiroshi Suzuki, Axial anomaly in the reduced model Higher representations, Journal of High Energy Physics, 7, 5, 973-992, 2003.05, The axial anomaly arising from the fermion sector of U (N) or SU(N) reduced model is studied under a certain restriction of gauge field configurations (the "U(1) embedding" with N = L^{d}). We use the overlap-Dirac operator and consider how the anomaly changes as a function of a gauge-group representation of the fermion. A simple argument shows that the anomaly vanishes for an irreducible representation expressed by a Young tableau whose number of boxes is a multiple of L^{2} (such as the adjoint representation) and for a tensor-product of them. We also evaluate the anomaly for general gauge-group representations in the large N limit. The large N limit exhibits expected algebraic properties as the axial anomaly. Nevertheless, when the gauge group is SU(N), it does not have a structure such as the trace of a product of traceless gauge-group generators which is expected from the corresponding gauge field theory.. |

95. | Kazuo Fujikawa, Masato Ishibashi, Hiroshi Suzuki, CP breaking in lattice chiral gauge theory, Nuclear Physics B - Proceedings Supplements, 10.1016/S0920-5632(03)80466-8, 119, 781-783, 2003.01, The CP symmetry is not manifestly implemented for the local and doubler-free Ginsparg-Wilson operator in lattice chiral gauge theory. We precisely identify where the effects of this CP breaking appear.. |

96. | Hiroshi Igarashi, Kiyoshi Okuyama, Hiroshi Suzuki, More about the axial anomaly on the lattice, Nuclear Physics B, 10.1016/S0550-3213(02)00812-X, 644, 1-2, 383-394, 2002.11, We study the axial anomaly defined on a finite-size lattice by using a Dirac operator which obeys the Ginsparg-Wilson relation. When the gauge group is U(1), we show that the basic structure of axial anomaly on the infinite lattice, which can be deduced by a cohomological analysis, persists even on (sufficiently large) finite-size lattices. For non-Abelian gauge groups, we propose a conjecture on a possible form of axial anomaly on the infinite lattice, which holds to all orders in perturbation theory. With this conjecture, we show that a structure of the axial anomaly on finite-size lattices is again basically identical to that on the infinite lattice. Our analysis with the Ginsparg-Wilson-Dirac operator indicates that, in appropriate frameworks, the basic structure of axial anomaly is quite robust and it persists even in a system with finite ultraviolet and infrared cutoffs.. |

97. | Takanori Fujiwara, Keiichi Nagao, Hiroshi Suzuki, Axial anomaly with the overlap-Dirac operator in arbitrary dimensions, Journal of High Energy Physics, 6, 9, 513-521, 2002.09, We evaluate for arbitrary even dimensions the classical continuum limit of the lattice axial anomaly defined by the overlap-Dirac operator. Our calculational scheme is simple and systematic. In particular, a powerful topological argument is utilized to determine the value of a lattice integral involved in the calculation. When the Dirac operator is free of species doubling, the classical continuum limit of the axial anomaly in various dimensions is combined into a form of the Chern character, as expected.. |

98. | Yoshio Kikukawa, Hiroshi Suzuki, Chiral anomalies in the reduced model, Journal of High Energy Physics, 6, 9, 649-668, 2002.09, On the basis of an observation due to Kiskis, Narayanan and Neuberger, we show that there is a remnant of chiral anomalies in the reduced model when a Dirac operator which obeys the Ginsparg-Wilson relation is employed for the fermion sector. We consider fermions belonging to the fundamental representation of the gauge group U (N) or SU(N). For vector-like theories, we determine a general form of the axial anomaly or the topological charge within a framework of a U(1) embedding. For chiral gauge theories with the gauge group U (N), a remnant of gauge anomaly emerges as an obstruction to a smooth fermion integration measure. The pure gauge action of gauge-field configurations which cause these non-trivial phenomena always diverges in the 't Hooft N → ∞ limit when d > 2.. |

99. | Axial anomaly with the overlap-Dirac operator in arbitrary dimensions We evaluate for arbitrary even dimensions the classical continuum limit of the lattice axial anomaly defined by the overlap-Dirac operator. Our calculational scheme is simple and systematic. In particular, a powerful topological argument is utilized to determine the value of a lattice integral involved in the calculation. When the Dirac operator is free of species doubling, the classical continuum limit of the axial anomaly in various dimensions is combined into a form of the Chern character, as expected.. |

100. | Chiral anomalies in the reduced model On the basis of an observation due to Kiskis, Narayanan and Neuberger, we show that there is a remnant of chiral anomalies in the reduced model when a Dirac operator which obeys the Ginsparg-Wilson relation is employed for the fermion sector. We consider fermions belonging to the fundamental representation of the gauge group U(N) or SU(N). For vector-like theories, we determine a general form of the axial anomaly or the topological charge within a framework of a U(1) embedding. For chiral gauge theories with the gauge group U(N), a remnant of gauge anomaly emerges as an obstruction to a smooth fermion integration measure. The pure gauge action of gauge-field configurations which cause these non-trivial phenomena always diverges in the 't Hooft $N oinfty$ limit when d>2.. |

101. | Kazuo Fujikawa, Masato Ishibashi, Hiroshi Suzuki, Ginsparg-Wilson operators and a no-go theorem, Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, 10.1016/S0370-2693(02)01936-6, 538, 1-2, 197-201, 2002.06, If one uses a general class of Ginsparg-Wilson operators, it is known that CP symmetry is spoiled in chiral gauge theory for a finite lattice spacing and the Majorana fermion is not defined in the presence of chiral symmetric Yukawa couplings. We summarize these properties in the form of a theorem for the general Ginsparg-Wilson relation.. |

102. | Kazuo Fujikawa, Masato Ishibashi, Hiroshi Suzuki, CP breaking in lattice chiral gauge theories, Journal of High Energy Physics, 6, 4, 1121-1145, 2002.04, The CP symmetry is not manifestly implemented for the local and doubler-free Ginsparg-Wilson operator in lattice chiral gauge theory. We precisely identify where the effects of this CP breaking appear. We show that they appear in: (I) Overall constant phase of the fermion generating functional. (II) Overall constant coefficient of the fermion generating functional. (Ill) Fermion propagator appearing in external fermion lines and the propagator connected to Yukawa vertices. The first effect appears from the transformation of the path integral measure and it is absorbed into a suitable definition of the constant phase factor for each topological sector; in this sense there appears no "CP anomaly". The second constant arises from the explicit breaking in the action and it is absorbed by the suitable weights with which topological sectors are summed. The last one in the propagator is inherent to this formulation and cannot be avoided by a mere modification of the projection operator, for example, in the framework of the Ginsparg-Wilson operator. This breaking emerges as an (almost) contact term in the propagator when the Higgs field, which is treated perturbatively, has no vacuum expectation value. In the presence of the vacuum expectation value, however, a completely new situation arises and the breaking becomes intrinsically non-local, though this breaking may still be removed in a suitable continuum limit. This non-local CP breaking is expected to persist for a non-perturbative treatment of the Higgs coupling.. |

103. | Yoshio Kikukawa, Yoichi Nakayama, Hiroshi Suzuki, On the lattice construction of electroweak gauge theory, Nuclear Physics B - Proceedings Supplements, 10.1016/S0920-5632(01)01837-0, 106-107, 763-765, 2002.03, Based on the Ginsparg-Wilson relation, a gauge invariant formulation of electroweak SU(2) × U(1) gauge theory on the lattice is considered. If the hypercharge gauge coupling is turned off in the vacuum sector of the U(1) gauge fields, the theory consists of four left-handed SU(2) doublets and it is possible, as in vector-like theories, to make the fermion measure defined globally in all topological sectors of SU(2). We then try to incorporate U(1) gauge field, following Lüscher's reconstruction theorem. The global integrability condition is proved for "gauge loops" in the space of the U(1) gauge fields with arbitrary SU(2) gauge field fixed in the background. For "non-gauge loops", however, the proof is given so far only for the classical SU(2) instanton backgrounds.. |

104. | CP breaking in lattice chiral gauge theories The CP symmetry is not manifestly implemented for the local and doubler-free Ginsparg-Wilson operator in lattice chiral gauge theory. We precisely identify where the effects of this CP breaking appear. We show that they appear in: (I) Overall constant phase of the fermion generating functional. (II) Overall constant coefficient of the fermion generating functional. (III) Fermion propagator appearing in external fermion lines and the propagator connected to Yukawa vertices. The first effect appears from the transformation of the path integral measure and it is absorbed into a suitable definition of the constant phase factor for each topological sector; in this sense there appears no ``CP anomaly''. The second constant arises from the explicit breaking in the action and it is absorbed by the suitable weights with which topological sectors are summed. The last one in the propagator is inherent to this formulation and cannot be avoided by a mere modification of the projection operator, for example, in the framework of the Ginsparg-Wilson operator. This breaking emerges as an (almost) contact term in the propagator when the Higgs field, which is treated perturbatively, has no vacuum expectation value. In the presence of the vacuum expectation value, however, a completely new situation arises and the breaking becomes intrinsically non-local, though this breaking may still be removed in a suitable continuum limit. This non-local CP breaking is expected to persist for a non-perturbative treatment of the Higgs coupling.. |

105. | On the lattice construction of electroweak gauge theory Based on the Ginsparg-Wilson relation, a gauge invariant formulation of electroweak SU(2)xU(1) gauge theory on the lattice is considered. If the hypercharge gauge coupling is turned off in the vacuum sector of the U(1) gauge fields, the theory consists of four left-handed SU(2) doublets and it is possible, as in vector-like theories, to make the fermion measure defined globally in all topological sectors of SU(2). We then try to incorporate U(1) gauge field, following L"uscher's reconstruction theorem. The global integrability condition is proved for ``gauge loops'' in the space of the U(1) gauge fields with arbitrary SU(2) gauge field fixed in the background. For ``non-gauge loops'', however, the proof is given so far only for the classical SU(2) instanton backgrounds.. |

106. | Takanori Fujiwara, Hiroshi Suzuki, Ke Wu, Topological charge of lattice Abelian gauge theory, Progress of Theoretical Physics, 10.1143/PTP.105.789, 105, 5, 789-807, 2001.05, The configuration space of abelian gauge theory on a periodic lattice becomes topologically disconnected when exceptional gauge field configurations are removed. It is possible to define a U(1)-bundle from the nonexceptional link variables by a smooth interpolation of the transition functions. The lattice analogue of the Chern character obtained using a cohomological technique based on noncommutative differential calculus is shown to give a topological charge related to the topological winding number of the U(1)-bundle.. |

107. | S. James Gates, Marcus T. Grisaru, Marcia E. Knutt, Silvia Penati, Hiroshi Suzuki, Supersymmetric gauge anomaly with general homotopic paths, Nuclear Physics B, 10.1016/S0550-3213(00)00676-3, 596, 1-2, 315-347, 2001.02, We use the method of Banerjee, Banerjee and Mitra and minimal homotopy paths to compute the consistent gauge anomaly for several superspace models of SSYM coupled to matter. We review the derivation of the anomaly for N=1 in four dimensions and then discuss the anomaly for two-dimensional models with (2,0) supersymmetry.. |

108. | Hiroshi Suzuki, Anomaly cancellation condition in lattice gauge theory, Nuclear Physics B, 10.1016/S0550-3213(00)00408-9, 585, 1-2, 471-513, 2000.10, We study the gauge anomaly A defined on a 4-dimensional infinite lattice while keeping the lattice spacing finite. We assume that (I) A depends smoothly and locally on the gauge potential, (II) A reproduces the gauge anomaly in the continuum theory in the classical continuum limit, and (III) U(1) gauge anomalies have a topological property. It is then shown that the gauge anomaly A can always be removed by local counterterms to all orders in powers of the gauge potential, leaving possible breakings proportional to the anomaly in the continuum theory. This follows from an analysis of nontrivial local solutions to the Wess-Zumino consistency condition in lattice gauge theory. Our result is applicable to the lattice chiral gauge theory based on the Ginsparg-Wilson Dirac operator, when the gauge field is sufficiently weak ∥U(n,μ)-1∥<ε′ , where U(n,μ) is the link variable and ε′ a certain small positive constant.. |

109. | Takanori Fujiwara, Takuya Hayashi, Hiroshi Suzuki, Ke Wu, Topological obstruction in block-spin transformations, Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, 10.1016/S0370-2693(00)00920-5, 488, 3-4, 428-434, 2000.09, Block-spin transformations from a fine lattice to a coarse one are shown to give rise to a one-to-one correspondence between the zero-modes of the Ginsparg-Wilson Dirac operator on the fine lattice and those on the coarse lattice. The index is then preserved under the blocking process. Such a one-to-one correspondence is violated and the block-spin transformation becomes necessarily ill-defined when the absolute value of the index is larger than 2rN, where N is the number of the sites on the coarse lattice and r is the dimension of the gauge group representation of the fermion variables. (C) 2000 Elsevier Science B.V.. |

110. | Real Representation in Chiral Gauge Theories on the Lattice The Weyl fermion belonging to the real representation of the gauge group provides a simple illustrative example for L"uscher's gauge-invariant lattice formulation of chiral gauge theories. We can explicitly construct the fermion integration measure globally over the gauge-field configuration space in the arbitrary topological sector; there is no global obstruction corresponding to the Witten anomaly. It is shown that this Weyl formulation is equivalent to a lattice formulation based on the Majorana (left--right-symmetric) fermion, in which the fermion partition function is given by the Pfaffian with a definite sign, up to physically irrelevant contact terms. This observation suggests a natural relative normalization of the fermion measure in different topological sectors for the Weyl fermion belonging to the complex representation.. |

111. | Takanori Fujiwara, Hiroshi Suzuki, Ke Wu, Non-commutative differential calculus and the axial anomaly in Abelian lattice gauge theories, Nuclear Physics B, 10.1016/S0550-3213(99)00706-3, 569, 1-3, 643-660, 2000.03, The axial anomaly in lattice gauge theories has a topological nature when the Dirac operator satisfies the Ginsparg-Wilson relation. We study the axial anomaly in Abelian gauge theories on an infinite hypercubic lattice by utilizing cohomological arguments. The crucial tool in our approach is the non-commutative differential calculus (NCDC) which makes the Leibniz rule of exterior derivatives valid on the lattice. The topological nature of the "Chern character" on the lattice becomes manifest in the context of NCDC. Our result provides an algebraic proof of Lüscher's theorem for a four-dimensional lattice and its generalization to arbitrary dimensions.. |

112. | Hiroshi Suzuki, Real representation in chiral gauge theories on the lattice, Journal of High Energy Physics, 4, 10 PART B, 1-16, 2000, The Weyl fermion belonging to the real representation of the gauge group provides a simple illustrative example for Luscher's gauge-invariant lattice formulation of chiral gauge theories. We can explicitly construct the fermion integration measure globally over the gauge-field configuration space in the arbitrary topological sector; there is no global obstruction corresponding to the Witten anomaly. It is shown that this Weyl formulation is equivalent to a lattice formulation based on the Majorana (left-right-symmetric) fermion, in which the fermion partition function is given by the pfaffian with a definite sign, up to physically irrelevant contact terms. This observation suggests a natural relative normalization of the fermion measure in different topological sectors for the Weyl fermion belonging to the complex representation.. |

113. | Takanori Fujiwara, Hiroshi Suzuki, Ke Wu, Axial anomaly in lattice abelian gauge theory in arbitrary dimensions, Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, 10.1016/S0370-2693(99)00956-9, 463, 1, 63-68, 1999.01, The axial anomaly of lattice abelian gauge theory on a hyper-cubic regular lattice in arbitrary even dimensions is investigated by applying the method of exterior differential calculus. The topological invariance, gauge invariance and locality of the axial anomaly determine the explicit form of the topological part. The anomaly is obtained up to a multiplicative constant for finite lattice spacing and can be interpreted as the Chern character of the abelian lattice gauge theory.. |

114. | Hiroshi Suzuki, Gauge invariant effective action in Abelian chiral gauge theory on the lattice, Progress of Theoretical Physics, 10.1143/PTP.101.1147, 101, 5, 1147-1154, 1999.01, Lüscher's recent formulation of Abelian chiral gauge theories on the lattice, in the vacuum (or perturbative) sector in infinite volume, is reinterpreted in terms of the lattice covariant regularization. The gauge invariance of the effective action and the integrability of the gauge current in anomaly-free cases become transparent. The real part of the effective action is simply one-hall that of the Dirac fermion and, when the Dirac operator behaves properly in the continuum limit, the imaginary part in this limit reproduces the η-invariant.. |

115. | Hiroshi Suzuki, Invariant regularization of supersymmetric chiral gauge theory, Progress of Theoretical Physics Supplement, 10.1143/PTPS.135.194, 135, 194-210, 1999.01, We present a regularization scheme which respects the supersymmetry and the maximal background gauge covariance in supersymmetric chiral gauge theories. When the anomaly cancellation condition is satisfied, the effective action in the superfield background field method automatically restores the gauge invariance without counterterms. The scheme also provides a background gauge covariant definition of composite operators that is especially useful in analyzing anomalies. We present several applications: The minimal consistent gauge anomaly; the super-chiral anomaly and the superconformal anomaly; as the corresponding anomalous commutators, the Konishi anomaly and an anomalous supersymmetric transformation law of the supercurrent (the "central extension" of N = 1 supersymmetry algebra) and of the R-current.. |

116. | Yoshihisa Ohshima, Kiyoshi Okuyama, Hiroshi Suzuki, Hirofumi Yasuta, Remark on the consistent gauge anomaly in supersymmetric theories, Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, 10.1016/S0370-2693(99)00585-7, 457, 4, 291-298, 1999.01, We present a direct field theoretical calculation of the consistent gauge anomaly in the superfield formalism, on the basis of a definition of the effective action through the covariant gauge current. The scheme is conceptually and technically simple and the gauge covariance in intermediate steps reduces calculational labors considerably. The resultant superfield anomaly, being proportional to the anomaly d^{abc} = trT^{a}{T^{b},T^{c}}, is minimal without supplementing any counterterms. Our anomaly coincides with the anomaly obtained by Marinković as the solution of the Wess-Zumino consistency condition.. |

117. | Hiroshi Suzuki, Simple evaluation of the chiral Jacobian with the overlap Dirac operator, Progress of Theoretical Physics, 10.1143/PTP.102.141, 102, 1, 141-147, 1999.01, The chiral Jacobian, which is defined with Neuberger's overlap Dirac operator of the lattice fermion, is explicitly evaluated in the continuum limit without expanding it in the gauge coupling constant. Our calculational scheme is simple and straightforward. We determine a coefficient of the chiral anomaly for general values of the mass parameter and the Wilson parameter of the overlap Dirac operator.. |

118. | Hiroshi Suzuki, Renormalon's contribution to effective couplings, Modern Physics Letters A, 10.1142/S0217732398002710, 13, 31, 2551-2558, 1998.10, When an asymptotically non-free theory possesses a mass parameter independent of the Λ parameter, the uv renormalon gives rise to nonperturbative contributions, to dimension-four operators and dimensionless couplings, thus has a "dual" effect of the instanton. We illustrate this phenomenon in O(N) symmetric massive λφ^{4}model in the 1/N expansion. This effect of uv renormalon is briefly compared with nonperturbative corrections in the magnetic picture of the Seiberg-Witten theory.. |

119. | Takuya Hayashi, Yoshihisa Ohshima, Kiyoshi Okuyama, Hiroshi Suzuki, Invariant regularization of supersymmetric chiral gauge theory, Progress of Theoretical Physics, 10.1143/PTP.100.627, 100, 3, 627-655, 1998.01, We formulate a manifestly supersymmetric gauge covariant regularization of supersymmetric chiral gauge theories. In our scheme, the effective action in the superfield background field method above one-loop is always supersymmetric and gauge invariant. The gauge anomaly has a covariant form and can emerge only in one-loop diagrams with all the external lines being the background gauge superfield. We also present several illustrative applications in the one-loop approximation: the self-energy part of the chiral multiplet and of the gauge multiplet; the super-chiral anomaly and the superconformal anomaly; as the corresponding anomalous commutators, the Konishi anomaly and an anomalous supersymmetric transformation law of the supercurrent (the "central extension" of N = 1 supersymmetry algebra) and of the R-current.. |

120. | Takuya Hayashi, Yoshihisa Ohshima, Kiyoshi Okuyama, Hiroshi Suzuki, Invariant regularization of supersymmetric chiral gauge theory. II, Progress of Theoretical Physics, 10.1143/PTP.100.1033, 100, 5, 1033-1054, 1998.01, By undertaking additional analyses postponed in a previous paper, we complete our construction of a manifestly supersymmetric gauge-covariant regularization of supersymmetric chiral gauge theories. We present the following: An evaluation of the covariant gauge anomaly; a proof of the integrability of the covariant gauge current in anomaly-free cases; a calculation of a one-loop superconformal anomaly in the gauge supermultiplet sector. On the last point, we find that the ghost-anti-ghost supermultiplet and the Nakanishi-Lautrup supermultiplet give rise to BRST exact contributions which, due to "tree-level" Slavnov-Taylor identities in our regularization scheme, can safely be neglected, at least at the one-loop level.. |

121. | Hiroshi Suzuki, Hirofumi Yasuta, Quantum bubble nucleation beyond the WKB approximation Resummation of vacuum bubble diagrams, Physical Review D - Particles, Fields, Gravitation and Cosmology, 10.1103/PhysRevD.57.2500, 57, 4, 2500-2506, 1998.01, On the basis of Borel resummation, we propose a systematical improvement of the bounce calculus of the quantum bubble nucleation rate. We study a metastable super-renormalizable field theory, (Formula presented)-dimensional, (Formula presented) symmetric (Formula presented) model (Formula presented) with an attractive interaction. The validity of our proposal is tested in (Formula presented) (quantum mechanics) by using the perturbation series of ground state energy to high orders. We also present a result in (Formula presented) based on an explicit calculation of vacuum bubble diagrams to five loop orders.. |

122. | Hiroshi Suzuki, Hirofumi Yasuta, Observing quantum tunneling in perturbation series, Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, 10.1016/S0370-2693(97)00368-7, 400, 3-4, 341-345, 1997.05, We apply Borel resummation to the conventional perturbation series of ground state energy in a metastable potential, V(x) = x^{2}/2 - gx^{4}/4. We observe numerically that the discontinuity of the Borel transform reproduces the imaginary part of the energy eigenvalue, i.e., the total decay width due to quantum tunneling. The agreement with the exact numerical value is remarkable in the whole tunneling regime 0 < g ≲ 0.7.. |

123. | Kazuo Fujikawa, Hiroshi Suzuki, Duality in potential curve crossing Application to quantum coherence, Physical Review A - Atomic, Molecular, and Optical Physics, 10.1103/PhysRevA.56.3436, 56, 5, 3436-3445, 1997.01, A field-dependent su(2) gauge transformation connects between the adiabatic and diabatic pictures in the (Landau-Zener-Stueckelberg) potential curve crossing. It is pointed out that weak and strong potential curve crossing interactions are interchanged under this transformation, thus realizing a naive strong and weak duality. A reliable perturbation theory should thus be formulated in limits of both weak and strong interactions. In fact, the main characteristics of the potential crossing phenomena such as the Landau-Zener formula including its numerical coefficient are well described by simple (time-independent) perturbation theory without referring to Stokes phenomena. We also show that quantum coherence in a double-well potential is generally suppressed by the effect of a potential curve crossing, which is analogous to the effect of Ohmic dissipation on quantum coherence.. |

124. | Kiyoshi Okuyama, Hiroshi Suzuki, Gauge invariant Pauli-Villars regularization of chiral fermions, Progress of Theoretical Physics, 10.1143/PTP.98.463, 98, 2, 463-484, 1997.01, We extend the idea of the generalized Pauli-Villars regularization of Frolov and Slavnov and analyze the general structure of the regularization scheme. The gauge anomaly-free condition emerges in a simple way in the scheme, and, under the standard prescription for the momentum assignment, the Pauli-Villars Lagrangian provides a gauge invariant regularization of chiral fermions in arbitrary anomaly-free representations. The vacuum polarization tensor is transverse, and the fermion number and the conformal anomalies have gauge invariant forms. We also point out that the real representation can be treated in a straightforward manner and the covariant regularization scheme is directly implemented.. |

125. | Kiyoshi Okuyama, Hiroshi Suzuki, Manifestly gauge covariant treatment of lattice chiral fermions. II, Physical Review D - Particles, Fields, Gravitation and Cosmology, 10.1103/PhysRevD.56.6829, 56, 11, 6829-6834, 1997.01, We propose a formulation of chiral fermions on a lattice, on the basis of a lattice extension of the covariant regularization scheme in continuum field theory. The species doublers do not emerge. The real part of the effective action is just one-half of that of Dirac-Wilson fermion and is always gauge invariant even with a finite lattice spacing. The gauge invariance of the imaginary part, on the other hand, sets a severe constraint that is a lattice analog of the gauge anomaly-free condition. For real gauge representations, the imaginary part identically vanishes and the gauge invariance becomes exact.. |

126. | Hiroshi Suzuki, Manifestly gauge covariant treatment of lattice chiral fermions, Physical Review D - Particles, Fields, Gravitation and Cosmology, 10.1103/PhysRevD.55.2994, 55, 5, 2994-2997, 1997.01, We propose a lattice formulation of the chiral fermion which maximally respects the gauge symmetry and simultaneously is free of the unwanted species doublers. The formulation is based on the lattice fermion propagator and composite operators, rather than on the lattice fermion action. The fermionic determinant is defined as a functional integral of an expectation value of the gauge current operator with respect to the background gauge field: The gauge anomaly is characterized as the nonintegrability. We perform some perturbative tests to confirm the gauge covariance and an absence of the doublers. The formulation can be applied rather straightforwardly to numerical simulations in the quenched approximation.. |

127. | Kazunobu Haga, Hiroshi Igarashi, Kiyoshi Okuyama, Hiroshi Suzuki, Remark on Pauli-Villars Lagrangian on the lattice, Physical Review D, 10.1103/PhysRevD.55.5325, 55, 9, 5325-5330, 1997.01, It is interesting to superimpose the Pauli-Villars regularization on the lattice regularization. We illustrate how this scheme works by evaluating the axial anomaly in a simple lattice fermion model, the Pauli-Villars Lagrangian with a gauge-noninvariant Wilson term. The gauge noninvariance of the axial anomaly, caused by the Wilson term, is remedied by a compensation among Pauli-Villars regulators in the continuum limit. A subtlety in the Frolov-Slavnov scheme for an odd number of chiral fermions in an anomaly-free complex gauge representation, which requires an infinite number of regulators, is briefly mentioned.. |

128. | Kiyoshi Okuyama, Hiroshi Suzuki, Path integral evaluation of non-abelian anomaly and Pauli-Villars-Gupta regularization, Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, 10.1016/0370-2693(96)00648-X, 382, 1-2, 117-123, 1996.08, When the path integral method of anomaly evaluation is applied to chiral gauge theories, two different types of gauge anomaly, i.e., the consistent form and the covariant form, appear depending on the regularization scheme for the Jacobian factor. We clarify the relation between the regularization scheme and the Pauli-Villars-Gupta (PVG) type Lagrangian level regularization. The conventional PVG, being non-gauge invariant for chiral gauge theories, in general corresponds to the consistent regularization scheme. The covariant regularization scheme, on the other hand, is realized by the generalized PVG Lagrangian recently proposed by Frolov and Slavnov. These correspondences are clarified by reformulating the PVG method as a regularization of the composite gauge current operator.. |

129. | Riccardo Guida, Kenichi Konishi, Hiroshi Suzuki, Improved convergence proof of the delta expansion and order dependent mappings, Annals of Physics, 10.1006/aphy.1996.0066, 249, 1, 109-145, 1996.07, We improve and generalize in several accounts the recent rigorous proof of convergence of delta expansion-order dependent mappings (variational perturbation expansion) for the energy eigenvalues of quartic anharmonic oscillator. For the single-well oscillator the uniformity of convergence in g∈[0, ∞] is proven. The convergence proof is extended also to complex values of g lying on a wide domain of the Riemann surface of E(g). Via the scaling relation à la Symanzik, this proves the convergence of delta expansion for the double well in the strong coupling regime (where the standard perturbation series is non Borel summable), as well as for the complex "energy eigenvalues" in certain metastable systems. Difficulties in extending the convergence proof to the cases of higher anharmonic oscillators are pointed out. Sufficient conditions for the convergence of delta expansion are summarized in the form of three general theorems, which should apply to a wide class of quantum mechanical and higher dimensional field theoretic systems.. |

130. | Ken Ichi Hiraizumi, Yoshihisa Ohshima, Hiroshi Suzuki, The hydrogen atom in strong electric fields Summation of the weak field series expansion, Physics Letters, Section A: General, Atomic and Solid State Physics, 10.1016/0375-9601(96)00243-5, 216, 1-5, 117-124, 1996.06, The order dependent mapping method, whose convergence has recently been proven for the energy eigenvalue of the anharmonic oscillator, is applied to re-sum the standard perturbation series for the Stark effect of the hydrogen atom. We perform a numerical experiment up to the 50th order of the perturbation expansion. A simple mapping, suggested by the analytic structure and the strong field behavior, gives an excellent agreement with the exact value for an intermediate range of the electric field, 0.03 (a.u.) ≤ E ≤ 0.25 (a.u.). The imaginary part of the energy (the decay width) as well as the real part of the energy is reproduced from the standard perturbation series.. |

131. | Renormalization group in 2 + ∈ dimensions and ∈ → 2: A simple model analysis Using a simple solvable model, i.e., the Higgs-Yukawa system with an infinite number of flavors, we explicitly demonstrate how a dimensional continuation of the β function in the two dimensional MS scheme fails to reproduce the correct behavior of the β function in four dimensions. The mapping between coupling constants in the two dimensional MS scheme and a conventional scheme in the cutoff regularization, in which the dimensional continuation of the β function is smooth, becomes singular when the dimension of spacetime approaches four. The existence of a non-trivial fixed point in 2 + ∈ dimensions continued to four dimensions (∈→2) in the two dimensional MS scheme is spurious and asymptotic safety cannot be imposed on this model in four dimensions.. |

132. | Super-Virasoro Anomaly, Super-Weyl Anomaly and the Super-Liouville Action for 2D Supergravity The relation between super-Virasoro anomaly and super-Weyl anomaly in $N=1$ NSR superstring coupled with 2D supergravity is investigated from canonical theoretical view point. The WZW action canceling the super-Virasoro anomaly is explicitly constructed. It is super-Weyl invariant but nonlocal functional of 2D supergravity. The nonlocality can be remedied by the super-Liouvlle action, which in turn recovers the super-Weyl anomaly. The final gravitational effective action turns out to be local but noncovariant super-Liouville action, describing the dynamical behavior of the super-Liouville fields. The BRST invariance of this approach is examined in the superconformal gauge and in the light-cone gauge.. |

133. | Hiroshi Suzuki, Calculation rule for Aoyama-Tamra's prescription for path integral with quantum tunneling, Modern Physics Letters A, 10.1142/S0217732396000047, 11, 1, 19-24, 1996.01, We derive a simple calculation rule for Aoyama-Tamra's prescription for path integral with degenerated potential minima. Nonperturbative corrections due to the restricted functional space (fundamental region) can systematically be computed with this rule. It becomes manifest that the prescription might give Borel summable series for finite temperature (or volume) system with quantum tunneling, while the advantage is lost at zero temperature (or infinite volume) limit.. |

134. | Nobuaki Nagao, Hiroshi Suzuki, Renormalization group in 2 + ∈ dimensions and ∈ → 2 A simple model analysis, Progress of Theoretical Physics, 10.1143/PTP.95.985, 95, 5, 985-993, 1996.01, Using a simple solvable model, i.e., the Higgs-Yukawa system with an infinite number of flavors, we explicitly demonstrate how a dimensional continuation of the β function in the two dimensional MS scheme fails to reproduce the correct behavior of the β function in four dimensions. The mapping between coupling constants in the two dimensional MS scheme and a conventional scheme in the cutoff regularization, in which the dimensional continuation of the β function is smooth, becomes singular when the dimension of spacetime approaches four. The existence of a non-trivial fixed point in 2 + ∈ dimensions continued to four dimensions (∈→2) in the two dimensional MS scheme is spurious and asymptotic safety cannot be imposed on this model in four dimensions.. |

135. | Riccardo Guida, Kenichi Konishi, Hiroshi Suzuki, Convergence of scaled delta expansion Anharmonic oscillator, Annals of Physics, 10.1006/aphy.1995.1059, 241, 1, 152-184, 1995.01, We prove that the linear delta expansion for energy eigenvalues of the quantum mechanical anharmonic oscillator converges to the exact answer if the order dependent trial frequency Ω is chosen to scale with the order as Ω = CN^{γ}; 1/3 < γ < 1/2, C > 0 as N → ∞. It converges also for γ = 1/3, if C ≥ α _{c}g ^{1/3}, α _{c}≃ 0.570875, where g is the coupling constant in front of the operator q ^{4}/4. The extreme case with γ = 1/3, C = γ _{c}g ^{1/3}corresponds to the choice discussed earlier by Seznec and Zinn-Justin and, more recently, by Duncan and Jones.. |

136. | Probability distribution functional in curved spaectime. |

137. | Hitoshi Murayama, Hiroshi Suzuki, T. Yanagida, Junichi Yokoyama, Chaotic inflation and baryogenesis in supergravity, Physical Review D, 10.1103/PhysRevD.50.R2356, 50, 4, 1994.01, We propose a Kähler potential in supergravity which successfully accommodates chaotic inflation. This model can have a large gravitino mass without giving a large mass to squarks and sleptons, and thus is free from both the gravitino problem and entropy crisis. In this model baryogenesis takes places naturally, identifying the inflaton with a right-handed sneutrino with its mass M1013 GeV, which is consistent with the COBE data and the Mikheyev-Smirnov-Wolfenstein solution to the solar neutrino problem. The model can also accommodate the matter content appropriate for the mixed dark matter scenario.. |

138. | Hiroshi Suzuki, Masahiro Tanaka, Flat directions in de Sitter space, Physical Review D, 10.1103/PhysRevD.49.6692, 49, 12, 6692-6704, 1994.01, The one loop level effective potential along the flat direction in global supersymmetric models is evaluated in de Sitter space. In flat space the direction φ only has a curvature determined by the supersymmetry soft breaking mass term m2φ2 and in the supersymmetric limit m→0 it receives no radiative corrections because of the nonrenormalization theorem. In this paper we show that in de Sitter space the one loop radiative correction induces a term ∼-3g2H2φ2 ln(φ2)/(16π2) on the flat direction, where g is a typical coupling constant and H is the Hubble parameter. If the (renormalized) curvature coupling is nearly zero, 0, and the soft breaking mass is sufficiently small as m2g2H2/π2, the correction may qualitatively modify the tree level potential and give an unbounded potential for the flat direction. We argue that this behavior is irrespective of the matter content and the details of the model if the flat direction couples to a scalar multiplet (as realistic supersymmetric models should do). The unbounded potential may give a large vacuum expectation value of φ in the inflationary expanding universe and be desirable for baryogenesis by the Affleck-Dine mechanism. Including the back reaction effect, the unbounded potential may also cause the adjustment mechanism for the cosmological constant problem.. |

139. | M. Sasaki, Hiroshi Suzuki, K. Yamamoto, J. Yokoyama, Superexpansionary divergence Breakdown of perturbative quantum field theory in spacetime with accelerated expansion, Classical and Quantum Gravity, 10.1088/0264-9381/10/5/003, 10, 5, 1993.12, The authors show that perturbative quantum field theory may break down in curved spacetime with accelerated expansion. They consider lambda phi ^{p}-theory (p=3,4,5,. . .) with curvature coupling xi R phi ^{2} in de Sitter space and perturbatively evaluate the n-point function. They find the vertex integral over all spacetime points diverges for a certain range of the mass and curvature coupling. In particular, for lambda phi ^{4} theory with xi =0, the divergence arises for m^{2}/H ^{2}_{16} where H^{-1} is the de Sitter radius. Then, they show that the same type of divergence arises quite generally in a spacetime with accelerated expansion. Since it is caused by unboundedly accelerated expansion of spacetime, they call it the superexpansionary divergence.. |

140. | Joaquim Gomis, Hiroshi Suzuki, Covariant currents in N = 2 super-Liouville theory, Nuclear Physics, Section B, 10.1016/0550-3213(93)90241-G, 393, 1-2, 126-148, 1993.03, Based on a path-integral prescription for anomaly calculation, we analyze an effective theory of the two-dimensional N = 2 supergravity, i.e. N = 2 super-Liouville theory. We calculate the anomalies associated with the BRST supercurrent and the ghost-number supercurrent. From those expressions of anomalies, we construct covariant BRST and ghost-number supercurrents in the effective theory. We then show that the (super-)coordinate BRST current algebra forms a superfield extension of the topological conformal algebra for an arbitrary type of conformal matter or, in terms of the string theory, for an arbitrary number of space-time dimensions. This fact is in great contrast with N = 0 and N = 1 (super-)Liouville theory, where the topological algebra singles out a particular value of dimensions. Our observation suggests a topological nature of the two-dimensional N = 2 supergravity as a quantum theory.. |

141. | H. Murayama, Hiroshi Suzuki, T. Yanagida, Jun'ichi Yokoyama, Chaotic inflation and baryogenesis by right-handed sneutrinos, Physical Review Letters, 10.1103/PhysRevLett.70.1912, 70, 13, 1912-1915, 1993.01, We present a model of chaotic inflation driven by the superpartner of the right-handed neutrino (NR). This model gives the correct magnitude of the density perturbation observed by the Cosmic Background Explorer satellite with a right-handed neutrino mass 1013 GeV, which is also preferred by the Mikheyev-Smirnov-Wolfenstein solution to the solar neutrino problem. The reheating process is the dacay of the coherently oscillating NR. This decay process also generates lepton asymmetry via CP violation, which will be converted to baryon asymmetry thanks to the electroweak anomaly. This model can incorporate the τ-neutrino mass 10 eV.. |

142. | H. Murayama, Hiroshi Suzuki, T. Yanagida, Radiative breaking of Peccei-Quinn symmetry at the intermediate mass scale, Physics Letters B, 10.1016/0370-2693(92)91397-R, 291, 4, 418-425, 1992.10, We construct a supersymmetric (SUSY) extension of an invisible axion model, in which the Peccei-Quinn symmetry is broken naturally at the intermediate mass scale 10^{10}-10^{12} GeV by radiative corrections from right-handed neutrino loops. The SUSY-invariant mass of doublet Higgs supermultiplets is forbidden by the Peccei-Quinn symmetry, whose breaking, however, generates an invariant Higgs mass of the order of the Fermi scale. In this model the right-handed neutrinos acquire large Majorana masses which are in a favored range for the Mikheyev-Smirnov-Wolfenstein solution to the solar neutrino problem.. |

143. | Joaquim Gomis, Hiroshi Suzuki, N = 2 string as a topological conformal theory, Physics Letters B, 10.1016/0370-2693(92)90191-6, 278, 3, 266-270, 1992.03, We prove that critical and subcritical N = 2 string theory gives a realization of an N = 2 superfield extension of the topological conformal algebra. The essential observation is the vanishing of the background ghost charge.. |

144. | Kazuo Fujikawa, Satoshi Iso, Misao Sasaki, Hiroshi Suzuki, Canonical formulation of quantum tunneling with dissipation, Physical Review Letters, 10.1103/PhysRevLett.68.1093, 68, 8, 1093-1096, 1992.01, The tunneling in a double-well potential with dissipation is formulated without referring to instantons. This formulation, in the domain of small dissipation, goes beyond the instanton approximation. Several applications of this formulation for the Ohmic case are presented, and we show that the virtual mixing of excited states induced by dissipative interactions tends to enhance the tunneling rate. This enhancement effect becomes dominant for a super-Ohmic case.. |

145. | Kazuo Fujikawa, Satoshi Iso, Misao Sasaki, Hiroshi Suzuki, Quantum tunneling with dissipation Possible enhancement by dissipative interactions, Physical Review B, 10.1103/PhysRevB.46.10295, 46, 16, 10295-10309, 1992.01, The macroscopic quantum tunneling in a double-well potential with dissipation is formulated without referring to instantons. This formulation, in the domain of small dissipation, goes beyond the instanton approximation which corresponds to the two-state truncated system (or, the so-called spin-boson Hamiltonian). It is first confirmed that our formulation, when applied to the two-state truncated system, reproduces all the known results of the instanton approximation. It is then shown that the ground state is mixed with excited states by dissipative interactions and this effect tends to enhance the ground-state quantum tunneling. In the Ohmic dissipation case this enhancement factor, even for a shallow double-well potential, can be at most comparable to the suppression factor which has been known from the work by Caldeira and Leggett. In the super-Ohmic case, however, the enhancement factor generally exceeds the suppression factor and the two-state approximation fails. A salient feature in the choice of counter terms in macroscopic quantum tunneling, which is essential to the above conclusion, is emphasized.. |

146. | Kazuhiro Yamamoto, Michiyasu Nagasawa, Misao Sasaki, Hiroshi Suzuki, Jun Ichi Yokoyama, Statistics of baryon isocurvature perturbations in the inflationary universe, Physical Review D, 10.1103/PhysRevD.46.4206, 46, 10, 4206-4217, 1992.01, The statistical distribution of baryon-number fluctuations, which may provide a proper initial condition for the minimal isocurvature scenario, is carefully investigated both analytically and numerically. For fluctuations associated with power-law inflation, we find that the distribution is highly non-Gaussian on scales of pregalactic star formation while it is Gaussian on scales of large-scale structure. On the other hand, in the pure de Sitter universe, it is shown to be Gaussian on any astrophysical scale. It is also discussed why the Gaussian nature appears in these models.. |

147. | Kazuo Fujikawa, Hiroshi Suzuki, Topological conformal algebra and BRST algebra in non-critical string theories, Nuclear Physics, Section B, 10.1016/0550-3213(91)90272-Y, 361, 2, 539-554, 1991.09, The operator algebra in non-critical string theories is studied by treating the cosmological term as a perturbation. The algebra of covariantly regularized BRST and related currents contains a twisted N = 2 superconformal algebra only at d = -2 in bosonic strings, and a twisted N = 3 superconformal algebra only at d = ±∞ in spinning strings. The bosonic string at d = -2 is examined by replacing the string coordinate by a fermionic matter with c = -2. The resulting bc-βγ system accommodates various forms of BRST cohomology, and the ghost number assignment and BRST cohomology are different in the c = -2 string theory and two-dimensional topological gravity.. |

148. | Misao Sasaki, Hiroshi Suzuki, Matrix realization of random surfaces, Physical Review D, 10.1103/PhysRevD.43.4015, 43, 12, 4015-4028, 1991.01, The large-N one-matrix model with a potential V()=22+g44N+g66N2 is carefully investigated using the orthogonal polynomial method. We present a numerical method to solve the recurrence relation and evaluate the recursion coefficients rk (k=1, 2, 3, ) of the orthogonal polynomials at large N. We find that for g6g42>12 there is no m=2 solution which can be expressed as a smooth function of kN in the limit N. This means that the assumption of smoothness of rk at N near the critical point, which was essential to derive the string susceptibility and the string equation, is broken even at the tree level of the genus expansion by adding the 6 term. We have also observed the free energy around the (expected) critical point to confirm that the system does not have the desired criticality as pure gravity. Our (discouraging) results for m=2 are complementary to previous analyses by the saddle-point method. On the other hand, for the case m=3 (g6g42=45), we find a well-behaved solution which coincides with the result obtained by Brézin, Marinari, and Parisi. To strengthen the validity of our numerical scheme, we present in an appendix a nonperturbative solution for m=1 which obeys the so-called type-II string equation.. |

149. | Kazuo Fujikawa, Takeshi Inagaki, Hiroshi Suzuki, BRS current and related anomalies in two-dimensional gravity and string theories, Nuclear Physics, Section B, 10.1016/0550-3213(90)90106-N, 332, 2, 499-529, 1990.03, The BRS currents in two-dimensional gravity and supergravity theories, which are related to string theory, contain anomalous terms. The origin of these anomalies can be neatly understood in a carefully defined path integral. We present the detailed calculations of these BRS and related anomalies in the holomorphic or anti-holomorphic sector separately in the conformal gauge. One-loop renormalization of the Liouville action becomes transparent in our formalation. We identify a BRS invariant BRS current (and thus nil-potent charge) and a conformally invariant ghost number current by incorporating the dynamical Weyl freedom explicitly. The formal path integral construction of various composite operators is also checked by using the operator product technique. Implications of these BRS analyses on possible non-critical string theories at d < 26 or d < 10 are briefly discussed.. |

150. | Kazuo Fujikawa, Naohito Nakazawa, Hiroshi Suzuki, The bosonic string at D<26 and the higgs mechanism, Physics Letters B, 10.1016/0370-2693(89)91712-7, 221, 3-4, 289-293, 1989.05, On the basis of a BRS invariant formulation of a free bosonic string at D<26, we analyse the structures of BRS and ghost number operators and the string vacua. The ghost number and the mass spectrum are naturally related to each other in this scheme. By using a string field theoretical technique, it is also shown that the Weyl freedom gives rise to an unphysical Higgs scalar, which is absorbed by the vector particle in the first excited level, thus realizing the Higgs mechanism.. |

151. | Kazuo Fujikawa, Takeshi Inagaki, Hiroshi Suzuki, BRS anomaly and the weyl freedom in string theory, Physics Letters B, 10.1016/0370-2693(88)91761-3, 213, 3, 279-284, 1988.10, It is shown that an anomalous correction to the BRS current ΔJ_{z}=( 3 4π)∂_{z}^{2}c^{z} in bosonic string theory essentially corresponds to the surface term ( 3 8π)sh{phonetic}∂_{α}(c^{α}√gR)d^{2}x in the anomalous jacobain factor. To make this correspondense explicit in the operator level, we present a quantization of a free string at D<26 which maintains the closure of the BRS symmetry.. |

152. | Atsushi Baba, Asobu Suzuki, Shinji Ejiri, Kazuyuki Kanaya, Masakiyo Kitazawa, Hiroshi Suzuki, Yusuke Taniguchi, Takashi Umeda, Calculation of PCAC mass with Wilson fermion using gradient flow, Proceedings of Science, LATTICE 2019, 191. |

153. | Kazuyuki Kanaya, Atsushi Baba, Asobu Suzuki, Shinji Ejiri, Masakiyo Kitazawa, Hiroshi Suzuki, Yusuke Taniguchi, Takashi Umeda, Study of 2+1 flavor finite-temperature QCD using improved Wilson quarks at the physical point with the gradient flow, Proceedings of Science, LATTICE 2019, 088. |

Unauthorized reprint of the contents of this database is prohibited.