### Abstract

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.

Original language | English |
---|---|

Article number | ptw153 |

Journal | Progress of Theoretical and Experimental Physics |

Volume | 2016 |

Issue number | 12 |

DOIs | |

Publication status | Published - 2016 Dec |

### Fingerprint

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Progress of Theoretical and Experimental Physics*,

*2016*(12), [ptw153]. https://doi.org/10.1093/ptep/ptw153

**Anomaly and sign problem in N = (2, 2) SYM on polyhedra : Numerical analysis.** / Kamata, Syo; Matsuura, So; Misumi, Tatsuhiro; Ohta, Kazutoshi.

Research output: Contribution to journal › Article

*Progress of Theoretical and Experimental Physics*, vol. 2016, no. 12, ptw153. https://doi.org/10.1093/ptep/ptw153

}

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

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.

UR - http://www.scopus.com/inward/record.url?scp=85074256336&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85074256336&partnerID=8YFLogxK

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 -