Perturbative Study of the Supersymmetric Lattice Theory from Matrix Model

TL;DR

This paper investigates a two-dimensional supersymmetric lattice Yang-Mills model using perturbative methods, confirming the absence of fine-tuning needs and highlighting supersymmetry's role in stabilizing the lattice structure.

Contribution

It provides an explicit perturbative analysis of the supersymmetric lattice model, demonstrating the vanishing of mass counter terms in the infinite volume limit and clarifying supersymmetry's stabilizing effect.

Findings

Mass counter terms vanish in the infinite volume limit.

Supersymmetry stabilizes the lattice space-time.

No fine-tuning is required for the theory.

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. We also find that the supersymmetry plays an important role in stabilizing the lattice space-time by the deconstruction.