Action principles, restoration of BRS symmetry and the renormalization group equation for chiral non-Abelian gauge theories in dimensional renormalization with a non-anticommuting $\gamma_5$

TL;DR

This paper thoroughly analyzes the one-loop renormalization of chiral non-Abelian gauge theories in dimensional renormalization, focusing on BRS symmetry restoration and deriving the renormalization group equation.

Contribution

It provides explicit calculations of anomalous terms, counterterms, and the renormalization group equation within a consistent dimensional renormalization framework for chiral gauge theories.

Findings

Computed anomalous term coefficients in Slavnov-Taylor equations

Derived counterterms for BRS symmetry restoration

Established the renormalization group equation in anomaly-free theories

Abstract

The one-loop renormalization of a general chiral gauge theory without scalar and Majorana fields is fully worked out within Breitenlohner and Maison dimensional renormalization scheme. The coefficients of the anomalous terms introduced in the Slavnov-Taylor equations by the minimal subtraction algorithm are calculated and the asymmetric counterterms needed to restore the BRS symmetry, if the anomaly cancellation conditions are met, are computed. The renormalization group equation and its coefficients are worked out in the anomaly free case. The computations draw heavily from the existence of action principles and BRS cohomology theory.