The fermion determinant in (4,4) 2d lattice super-Yang-Mills

TL;DR

This paper investigates the sign problem in lattice formulations of (4,4) 2D super-Yang-Mills, revealing that the fermion determinant is not always positive, which impacts simulation approaches.

Contribution

It demonstrates that the fermion determinant in certain lattice supersymmetric actions can be non-positive, highlighting a challenge for numerical simulations of these theories.

Findings

Fermion determinant is not generally positive in the studied lattice actions.

Implications for lattice simulation methods due to the sign problem.

Preliminary phase analysis of the fermion determinant in the phase-quenched ensemble.

Abstract

We find that the fermion determinant is not generally positive in a class of lattice actions recently constructed by Cohen et al. [hep-lat/0307012]; these are actions that contain an exact lattice supersymmetry and have as their target (continuum) theory (4,4) 2-dimensional super-Yang-Mills. We discuss the implications of this finding for lattice simulations and give some preliminary results for the phase of the determinant in the phase-quenched ensemble.