Ward identities in $\mathcal{N}=1$ supersymmetric SU(3) Yang-Mills theory on the lattice

TL;DR

This paper investigates how supersymmetric Ward identities on the lattice can be used to identify the critical parameters where supersymmetry is restored in $ ext{SU}(3)$ Yang-Mills theory with gluinos.

Contribution

It introduces a method to determine the critical hopping parameter on the lattice by employing SUSY Ward identities, aiding in the restoration of supersymmetry in lattice simulations.

Findings

Identification of the critical hopping parameter for supersymmetry restoration.

Demonstration of lattice Ward identities as a tool for symmetry analysis.

Insights into the soft breaking effects due to gluino mass.

Abstract

The introduction of a space-time lattice as a regulator of field theories breaks symmetries associated with continuous space-time, i.e.\ Poincar{\'e} invariance and supersymmetry. A non-zero gluino mass in the supersymmetric Yang-Mills theory causes an additional soft breaking of supersymmetry. We employ the lattice form of SUSY Ward identities, imposing that their continuum form would be recovered when removing the lattice regulator, to obtain the critical hopping parameter where broken symmetries can be recovered.