Perturbative Study of the Supersymmetric Lattice Model from Matrix Model

TL;DR

This paper performs a perturbative analysis of a supersymmetric lattice Yang-Mills model in two dimensions, confirming that it requires no fine-tuning in the infinite volume limit due to vanishing mass counter terms.

Contribution

It provides an explicit perturbative verification of the absence of susy-breaking counter terms and vacuum instability in the lattice model, including treatment of zero modes.

Findings

Mass counter terms vanish in the infinite volume limit.

The model requires no fine-tuning for supersymmetry preservation.

Infra-red divergences are avoided by introducing fermion masses and nonperturbative zero mode treatment.

Abstract

We study the lattice model for the supersymmetric Yang-Mills theory in two dimensions proposed by Cohen, Kaplan, Katz, and Unsal. We re-examine the formal proof for the absence of susy breaking counter terms as well as the stability of the vacuum by an explicit perturbative calculation for the case of U(2) gauge group. Introducing fermion masses and treating the bosonic zero momentum mode nonperturbatively, we avoid the infra-red divergences in the perturbative calculation. As a result, we find that there appear mass counter terms for finite volume which vanish in the infinite volume limit so that the theory needs no fine-tuning.