Supercurrent Renormalization in $\mathcal{N}=1$ Supersymmetric Yang-Mills Theory

TL;DR

This paper investigates the renormalization of the supercurrent in $ ext{N}=1$ supersymmetric Yang-Mills theory on the lattice, combining analytical and numerical methods to understand operator mixing and SUSY breaking effects.

Contribution

It introduces a comprehensive approach to renormalize the supercurrent on the lattice, including conversion factors and mixing with gauge-noninvariant operators, aiding SUSY studies.

Findings

Preliminary numerical results on operator mixing.

One-loop lattice perturbation theory calculations.

Insights into SUSY breaking on the lattice.

Abstract

In this work we study the renormalization of the SUSY Noether current in Supersymmetric $\mathcal{N}$ = 1 Yang-Mills (SYM) theory on the lattice. In particular, we study the mixing of the current with all other compatible operators of dimension 7/2 and 5/2, leading from the lattice-regularized to the $\overline{\rm MS}$-renormalized operator basis. We perform our task in two ways: (a) We compute, in dimensional regularization, the conversion factors relating the $\overline{\rm MS}$ scheme to an intermediate gauge-invariant coordinate-space scheme. In this second scheme, renormalization can be performed via lattice simulations. This could help to investigate the breaking of SUSY on the lattice and strategies towards simulations of supersymmetric QCD. Here we present some preliminary numerical results. (b) We use lattice perturbation theory and compute, to one loop, various two- and three-point functions. We consider mixing with all relevant gauge-noninvariant operators, which contain also ghost fields.