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

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.