Nonperturbative renormalization of the supercurrent in $\mathcal{N} = 1$ Supersymmetric Yang-Mills Theory

TL;DR

This paper develops a gauge-invariant nonperturbative renormalization method for the supercurrent in $ =1$ SYM theory, effectively addressing operator mixing issues caused by lattice supersymmetry breaking.

Contribution

It introduces a gauge-invariant renormalization scheme (GIRS) for the supercurrent, providing a practical approach to handle operator mixing in lattice supersymmetric theories.

Findings

Successfully addresses supercurrent mixing with other operators.

Provides nonperturbative renormalization factors in GIRS.

Calculates the conversion to the $ar{ m MS}$ scheme at one-loop.

Abstract

In this work, we study the nonperturbative renormalization of the supercurrent operator in $\mathcal{N} = 1$ Supersymmetric Yang-Mills (SYM) theory, using a gauge-invariant renormalization scheme (GIRS). The proposed prescription addresses successfully the unwanted mixing of the supercurrent with other operators of equal or lower dimension, which respect the same global symmetries. This mixing is introduced by the unavoidable breaking of supersymmetry on the lattice. In GIRS all gauge-noninvariant operators, which mix with the supercurrent, are excluded from the renormalization procedure. The one remaining mixing operator is accessible by numerical simulations. We present results for the renormalization of the supercurrent using a GIRS scheme. We also compute at one-loop order the conversion matrix which relates the nonperturbative renormalization factors in GIRS to the reference scheme $\bar{\rm MS}$.