Supercurrent renormalization of $\mathcal{N}=1$ supersymmetric Yang-Mills theory on the lattice

TL;DR

This paper investigates the renormalization of the supercurrent in lattice $ ext{N}=1$ Super-Yang Mills theory, aiming to restore supersymmetry in the continuum limit through gauge-invariant renormalization and scheme conversion.

Contribution

It provides the first lattice determination of the supercurrent renormalization factors and conversion to the $ ext{MS}$ scheme for $ ext{N}=1$ Super-Yang Mills theory.

Findings

Renormalization factors for the supercurrent are obtained.

Conversion factors to the $ ext{MS}$ scheme are provided.

Results facilitate supersymmetry restoration in lattice simulations.

Abstract

Supersymmetry on the lattice is explicitly broken by the gluino mass and lattice artifacts. However, it can be restored in the continuum limit by fine tuning the parameters based on the renormalized Ward identities. On the renormalization step not only the mass but also the renormalization of the supercurrent needs to be addressed. Here we present a lattice investigation to obtain the renormalization factors of the supercurrent for $\mathcal{N}$=1 Super-Yang Mills theory in a gauge invariant renormalization scheme. We also provide the conversion factors which are necessary in order to translate our results to the more standard $\overline{\text{MS}}$ scheme.