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

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.