On the restoration of supersymmetry in twisted two-dimensional lattice Yang-Mills theory

TL;DR

This paper investigates a lattice formulation of 2D super Yang-Mills theory with exact supersymmetry, demonstrating through simulations that additional supersymmetries and rotational invariance are restored in the continuum limit, and analyzing scalar eigenvalue distributions.

Contribution

It derives the action of twisted supersymmetries on component fields and provides numerical evidence for their restoration without fine tuning in the continuum limit.

Findings

Additional supersymmetries are restored in the continuum limit.

Twisted rotational invariance is supported to be restored.

Scalar eigenvalue distributions show power law tails, indicating quantum effects on classical moduli space.

Abstract

We study a discretization of ${\cal N}=2$ super Yang-Mills theory which possesses a single exact supersymmetry at non-zero lattice spacing. This supersymmetry arises after a reformulation of the theory in terms of {\it twisted} fields. In this paper we derive the action of the other twisted supersymmetries on the component fields and study, using Monte Carlo simulation, a series of corresponding Ward identities. Our results for SU(2) and SU(3) support a restoration of these additional supersymmetries without fine tuning in the infinite volume continuum limit. Additionally we present evidence supporting a restoration of (twisted) rotational invariance in the same limit. Finally we have examined the distribution of scalar field eigenvalues and find evidence for power law tails extending out to large eigenvalue. We argue that these tails indicate that the classical moduli space does not survive in the quantum theory.