Perturbative renormalization of the supercurrent operator in lattice ${\cal N}{=}1$ supersymmetric Yang-Mills theory

TL;DR

This paper performs a one-loop perturbative analysis of the supercurrent operator in lattice ${ m N}=1$ supersymmetric Yang-Mills theory, determining renormalization and mixing coefficients to aid nonperturbative studies.

Contribution

It provides the first detailed calculation of supercurrent operator renormalization and mixing coefficients on the lattice at one-loop order, including comparison between dimensional and lattice regularizations.

Findings

Calculated renormalization and mixing coefficients in $ar{MS}$ scheme.

Derived lattice renormalization factors for supercurrent operators.

Provided results applicable to nonperturbative supersymmetric Ward identity studies.

Abstract

In this work we perform a perturbative study of the Noether supercurrent operator in the context of Supersymmetric ${\cal N}{=}1$ Yang-Mills (SYM) theory on the lattice. The supercurrent mixes with several other operators, some of which are not gauge invariant, having the same quantum numbers. We determine, to one loop order, the renormalization and all corresponding mixing coefficients by computing relevant Green's functions of each one of the mixing operators with external elementary fields. Our calculations are performed both in dimensional and lattice regularization. From the first regularization we obtain the $\bar{MS}$-renormalized Green's functions; comparison of the latter with the corresponding Green's functions in the lattice regularization leads to the extraction of the lattice renormalization factors and mixing coefficients in the $\bar{MS}$ scheme. The lattice calculations are performed to lowest order in the lattice spacing, using Wilson gluons and clover improved gluinos. The lattice results can be used in nonperturbative studies of supersymmetric Ward identities.