Restoration of supersymmetry on the lattice: Two-dimensional $\mathcal{N}=(2,2)$ supersymmetric Yang-Mills theory

TL;DR

This study numerically confirms the restoration of supersymmetry in a two-dimensional lattice formulation of $ ext{SU}(2)$ Yang-Mills theory with a scalar mass term, highlighting the importance of supercurrent conservation.

Contribution

It demonstrates supersymmetry restoration on the lattice through supercurrent conservation, addressing subtleties in the massless case and validating Sugino's formulation.

Findings

Supersymmetry is restored with a scalar mass term.

Supercurrent conservation confirms supersymmetry restoration.

Subtleties in the massless case affect perturbative analysis.

Abstract

By numerically investigating the conservation law of the supercurrent, we confirm the restoration of supersymmetry in Sugino's lattice formulation of the two-dimensional $\mathcal{N}=(2,2)$ supersymmetric SU(2) Yang-Mills theory with a scalar mass term. Subtlety in the case without the scalar mass term, that appears to ruin perturbative power counting, is also pointed out.