Analysis of Ward identities in supersymmetric Yang-Mills theory

TL;DR

This paper introduces an improved numerical method for analyzing supersymmetric Ward identities in lattice supersymmetric Yang-Mills theory, demonstrating that lattice artifacts diminish as the square of the lattice spacing, consistent with theoretical predictions.

Contribution

It presents the first comprehensive analysis of supersymmetric Ward identities in SU(3) gauge theory on the lattice using an enhanced correlation-aware method.

Findings

Lattice artifacts scale as O(a^2) towards the continuum limit.

The method accounts for correlations between observables.

Results align with theoretical expectations.

Abstract

In numerical investigations of supersymmetric Yang-Mills theory on a lattice, the supersymmetric Ward identities are valuable for finding the critical value of the hopping parameter and for examining the size of supersymmetry breaking by the lattice discretisation. In this article we present an improved method for the numerical analysis of supersymmetric Ward identities, which takes into account the correlations between the various observables involved. We present the first complete analysis of supersymmetric Ward identities in $\mathcal{N}=1$ supersymmetric Yang-Mills theory with gauge group SU(3). The results show that lattice artefacts scale to zero as $O(a^2)$ towards the continuum limit in agreement with theoretical expectations.