Gauge-invariant Renormalization of the Gluino-Glue operator

TL;DR

This paper develops a gauge-invariant renormalization scheme for the Gluino-Glue operator in ${ m N}=1$ SYM theory, enabling accurate lattice computations of bound states by relating GIRS to the $ m ar{MS}$ scheme.

Contribution

It introduces a gauge-invariant renormalization scheme for the Gluino-Glue operator and calculates the one-loop conversion factor to the $ m ar{MS}$ scheme.

Findings

Computed the Green's function of two Gluino-Glue operators at distinct points.

Derived the one-loop conversion factor between GIRS and $ m ar{MS}$ schemes.

Facilitates nonperturbative lattice studies of bound states in supersymmetric Yang-Mills theory.

Abstract

We study the Gluino-Glue operator in the context of Supersymmetric ${\cal N}{=}1$ Yang-Mills (SYM) theory. This composite operator is gauge invariant, and it is directly connected to light bound states of the theory; its renormalization is very important as a necessary step for the study of low-lying bound states via numerical simulations. We make use of a Gauge-Invariant Renormalization Scheme (GIRS). This requires the calculation of the Green's function of a product of two Gluino-Glue operators, situated at distinct space-time points. Within this scheme, the mixing with non-gauge invariant operators which have the same quantum numbers is inconsequential. We compute the one-loop conversion factor relating the GIRS scheme to $\overline{\rm MS}$. This conversion factor can be used in order to convert to $\overline{\rm MS}$ Green's functions which are obtained via lattice simulations and are renormalized nonperturbatively in GIRS.