TY - JOUR

T1 - Anomaly and sign problem in N = (2, 2) SYM on polyhedra

T2 - Numerical analysis

AU - Kamata, Syo

AU - Matsuura, So

AU - Misumi, Tatsuhiro

AU - Ohta, Kazutoshi

N1 - Funding Information:
We would like to thank D. Kadoh, N. Sakai, and F. Sugino for useful discussions and comments. K.O. also would like to thank K. Sakai andY. Sasai for friendly discussions. S.M. also would like to thank P. H. Damgaard, A. Joseph, and S. Matsuura for useful discussions and people at the Niels Bohr Institute for their hospitality during his stay. S.K. also would like to thank Y. Kikukawa for helpful comments. The work of S.M., T.M., and K.O. was supported in part by Grant-in-Aid for Scientific Research (C) 15K05060, Grant-in-Aid for Young Scientists (B) 16K17677, and JSPS KAKENHI Grant Number JP26400256, respectively. S.K. is supported by the Advanced Science Measurement Research Center at Rikkyo University. This work is also supported by the MEXT-Supported Program for the Strategic Research Foundation at Private Universities “Topological Science” (Grant No. S1511006).
Publisher Copyright:
© The Author(s) 2016.

PY - 2016/12

Y1 - 2016/12

N2 - We investigate two-dimensional N = (2, 2) supersymmetric Yang–Mills (SYM) theory on discretized curved space (polyhedra). We first revisit that the number of supersymmetries of the continuum N = (2, 2) SYM theory on any curved manifold can be enhanced at least to two by introducing an appropriate U(1) gauge background associated with the U(1)V symmetry. We then show that the generalized Sugino model on discretized curved space, which was proposed in our previous work, can be identified with the discretization of this SUSY enhanced theory, where one of the supersymmetries remains, and the other is broken but restored in the continuum limit. We find that the U(1)A anomaly exists also in discretized theory as a result of an unbalance in the number of fermions proportional to the Euler characteristic of the polyhedra. We then study this model by using the numerical Monte Carlo simulation. We propose a novel phase-quench method called the “anomaly-phase-quenched approximation” with respect to the U(1)A anomaly. We show numerically that the Ward–Takahashi identity associated with the remaining supersymmetry is realized by adopting this approximation. We work out the relation between the sign (phase) problem and pseudo-zero-modes of the Dirac operator. We also show that the divergent behavior of the scalar one-point function gets milder as the genus of the background increases. These are the first numerical observations for the supersymmetric lattice model on curved space with generic topologies.

AB - We investigate two-dimensional N = (2, 2) supersymmetric Yang–Mills (SYM) theory on discretized curved space (polyhedra). We first revisit that the number of supersymmetries of the continuum N = (2, 2) SYM theory on any curved manifold can be enhanced at least to two by introducing an appropriate U(1) gauge background associated with the U(1)V symmetry. We then show that the generalized Sugino model on discretized curved space, which was proposed in our previous work, can be identified with the discretization of this SUSY enhanced theory, where one of the supersymmetries remains, and the other is broken but restored in the continuum limit. We find that the U(1)A anomaly exists also in discretized theory as a result of an unbalance in the number of fermions proportional to the Euler characteristic of the polyhedra. We then study this model by using the numerical Monte Carlo simulation. We propose a novel phase-quench method called the “anomaly-phase-quenched approximation” with respect to the U(1)A anomaly. We show numerically that the Ward–Takahashi identity associated with the remaining supersymmetry is realized by adopting this approximation. We work out the relation between the sign (phase) problem and pseudo-zero-modes of the Dirac operator. We also show that the divergent behavior of the scalar one-point function gets milder as the genus of the background increases. These are the first numerical observations for the supersymmetric lattice model on curved space with generic topologies.

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U2 - 10.1093/ptep/ptw153

DO - 10.1093/ptep/ptw153

M3 - Article

AN - SCOPUS:85074256336

VL - 2016

JO - Progress of Theoretical and Experimental Physics

JF - Progress of Theoretical and Experimental Physics

SN - 2050-3911

IS - 12

M1 - ptw153

ER -