Yang-Mills gauge anomalies in the presence of gravity with torsion

TL;DR

This paper investigates Yang-Mills gauge anomalies within gravitational theories that include torsion, utilizing BRST symmetry and Maurer-Cartan conditions to analyze anomalies and consistency conditions.

Contribution

It introduces a method to analyze gauge anomalies in gravity with torsion using BRST transformations and Maurer-Cartan horizontality conditions, providing new insights into anomaly structures.

Findings

Derived BRST transformations for Yang-Mills fields with torsion.

Solved Wess-Zumino consistency conditions for anomalies.

Clarified the role of Maurer-Cartan conditions in anomaly analysis.

Abstract

The BRST transformations for the Yang-Mills gauge fields in the presence of gravity with torsion are discussed by using the so-called Maurer-Cartan horizontality conditions. With the help of an operator $\d$ which allows to decompose the exterior spacetime derivative as a BRST commutator we solve the Wess-Zumino consistency condition corresponding to invariant Chern-Simons terms and gauge anomalies.