Flow Equations for the Relevant Part of the Pure Yang-Mills Action

TL;DR

This paper derives and integrates Wilson's exact renormalization group equations for the relevant part of pure Yang-Mills theory, analyzing how modified Slavnov-Taylor identities control BRST invariance breaking and gluon mass generation at finite infrared cutoff.

Contribution

It introduces a detailed analysis of the interplay between renormalization group flow and Slavnov-Taylor identities in Yang-Mills theory with a finite cutoff.

Findings

Modified Slavnov-Taylor identities control BRST invariance breaking.

Gluon mass term arises at finite infrared cutoff.

Framework allows for consistent truncation of the effective action.

Abstract

Wilson's exact renormalization group equations are derived and integrated for the relevant part of the pure Yang-Mills action. We discuss in detail how modified Slavnov-Taylor identities controle the breaking of BRST invariance in the presence of a finite infrared cutoff $k$ through relations among different parameters in the effective action. In particular they imply a nonvanishing gluon mass term for nonvanishing $k$. The requirement of consistency between the renormalization group flow and the modified Slavnov- Taylor identities allows to control the self-consistency of truncations of the effective action.