Absence of sign problem in two-dimensional N=(2,2) super Yang-Mills on lattice

TL;DR

This paper demonstrates that two-dimensional N=(2,2) super Yang-Mills theory on the lattice does not suffer from a sign problem in the continuum limit, confirming the validity of phase-quenched simulations for these models.

Contribution

It shows the absence of the sign problem in specific lattice formulations of N=(2,2) super Yang-Mills theory and explains discrepancies in previous studies.

Findings

Sign problem is absent in both CKKU and Sugino models.

Both models converge to the same continuum limit without fine tuning.

Previous claims of sign problem are explained as not capturing continuum physics.

Abstract

We show that N=(2,2) SU(N) super Yang-Mills theory on lattice does not have sign problem in the continuum limit, that is, under the phase-quenched simulation phase of the determinant localizes to 1 and hence the phase-quench approximation becomes exact. Among several formulations, we study models by Cohen-Kaplan-Katz-Unsal (CKKU) and by Sugino. We confirm that the sign problem is absent in both models and that they converge to the identical continuum limit without fine tuning. We provide a simple explanation why previous works by other authors, which claim an existence of the sign problem, do not capture the continuum physics.