On the sign problem in 2D lattice super Yang--Mills

TL;DR

This paper investigates whether certain supersymmetric lattice theories in two dimensions have a sign problem, finding evidence they do not in the continuum limit, which supports their use for studying non-perturbative supersymmetric gauge theories.

Contribution

The study provides the first numerical evidence that twisted lattice formulations of 2D supersymmetric Yang--Mills theories avoid the sign problem in the continuum limit.

Findings

No sign problem observed in continuum limit

Supports use of lattice formulations for non-perturbative studies

Applicable to theories with N=(2, 2) and N=(8, 8) supersymmetry

Abstract

In recent years a new class of supersymmetric lattice theories have been proposed which retain one or more exact supersymmetries for non-zero lattice spacing. Recently there has been some controversy in the literature concerning whether these theories suffer from a sign problem. In this paper we address this issue by conducting simulations of the N=(2, 2) and N=(8, 8) supersymmetric Yang--Mills theories in two dimensions for the U(N) theories with N=2,3,4, using the new twisted lattice formulations. Our results provide evidence that these theories do not suffer from a sign problem in the continuum limit. These results thus boost confidence that the new lattice formulations can be used successfully to explore non-perturbative aspects of four-dimensional N=4 supersymmetric Yang--Mills theory.