Investigating the sign problem for two-dimensional N = (2,2) and N = (8,8) lattice super Yang–Mills theories

Recently there has been some controversy in the literature concerning the existence of a fermion sign problem in the N = (2,2) supersymmetric Yang–Mills (SYM) theories on the lattice. In this work, we address this issue by conducting Monte Carlo simulations not only for N = (2,2) but also for N = (8,8) SYM in two dimensions for the U(N) theories with N = 2, using the new ideas derived from topological twisting followed by geometric discretization. Our results from simulations provide the evidence that these theories do not suffer from a sign problem as the continuum limit is approached. These results thus boost confidence that these new lattice formulations can be used successfully to explore the nonperturbative aspects of the four-dimensional N = 4 SYM theory.