Flow Equations and BRS Invariance for Yang-Mills Theories

TL;DR

This paper develops flow equations for Yang-Mills theories with an infrared cutoff, deriving modified Slavnov-Taylor identities to maintain BRS invariance and enabling non-perturbative analysis of gauge theories.

Contribution

It introduces modified Slavnov-Taylor identities for flow equations with an infrared cutoff, ensuring BRS invariance as the cutoff approaches zero.

Findings

Derived flow equations for effective action with cutoff

Established modified Slavnov-Taylor identities for non-zero cutoff

Obtained a $k$-dependent gauge field mass equation

Abstract

Flow equations describe the evolution of the effective action $\Gamma_k$ in the process of varying an infrared cutoff $k$. The presence of the infrared cutoff explicitly breaks gauge and hence BRS invariance. We derive modified Slavnov-Taylor identities, which are valid for nonvanishing $k$. They guarantee the BRS invariance of $\Gamma_k$ for $k\to0$, and hence allow the study of non-abelian gauge theories by integrating the flow equations. Within a perturbative expansion of $\Gamma_k$, we derive an equation for a $k$ dependent mass term for the gauge fields implied by the modified Slavnov-Taylor identities.