1. |
Abe, Motokazu, Morikawa, Okuto, Suzuki, Hiroshi, Fractional topological charge in lattice Abelian gauge theory, *Progress of Theoretical and Experimental Physics*, 10.1093/ptep/ptad009, 2023, 2, 2023.02. |

2. |
Kazuyuki Kanaya, Ryo Ashikawa, Shinji Ejiri, Masakiyo Kitazawa, Hiroshi Suzuki, Naoki Wakabayashi, Phase structure and critical point in heavy-quark QCD at finite temperature, *Proceedings of The 39th International Symposium on Lattice Field Theory — PoS(LATTICE2022)*, 10.22323/1.430.0177, 2023.01. |

3. |
Ishikawa, Kosuke, Morikawa, Okuto, Nakayama, Akira, Shibata, Kazuya, Suzuki, Hiroshi, Takaura, Hiromasa, Infrared renormalon in the supersymmetric $mathbb{C}P^{N-1}$ model on $mathbb{R} imes S^1$, *PTEP*, 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 ℂPN-1 model on ℝ × S1 with the ℤN twisted boundary conditions. In our large-N limit, the combination ΛR, where Λ is the dynamical scale and R is the S1 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 × S1, we find that the Borel singularity at u = 2, which exists in the system on the uncompactified ℝ2 and corresponds to twice the minimal bion action, disappears. Instead, an unfamiliar renormalon singularity emerges at u = 3/2 for the compactified space ℝ × S1. 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 × S1 prompts reconsideration on the semi-classical bion picture of the infrared renormalon.. |

4. |
Renormalon-free definition of the gluon condensate within the large-$eta_0$ 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.. |

5. |
One-loop perturbative coupling of A and A ∗ through the chiral overlap operator © 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.. |

6. |
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.. |

7. |
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.. |

8. |
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. |

9. |
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.. |

10. |
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.. |

11. |
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.. |

12. |
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.. |

13. |
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.. |

14. |
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.. |

15. |
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.. |

16. |
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.. |

17. |
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.. |

18. |
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.. |

19. |
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.. |

20. |
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.. |

21. |
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.. |

22. |
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.. |

23. |
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.. |

24. |
Probability distribution functional in curved spaectime. |