On the Geometrical Structure of Covariant Anomalies in Yang-Mills Theory

TL;DR

This paper explores the geometric structure of covariant anomalies in Yang-Mills theory, deriving new descent equations and clarifying the relationship between different anomaly formulations using a geometric BRS algebra.

Contribution

It introduces a new set of descent equations for covariant anomalies and provides a geometric realization of the BRS algebra to unify different anomaly approaches.

Findings

Derived new descent equations including covariant anomalies.

Determined counterterms linking consistent and covariant anomalies.

Presented a geometric BRS/anti-BRS algebra framework.

Abstract

Covariant anomalies are studied in terms of the theory of secondary characteristic classes of the universal bundle of Yang-Mills theory. A new set of descent equations is derived which contains the covariant current anomaly and the covariant Schwinger term. The counterterms relating consistent and covariant anomalies are determined. A geometrical realization of the BRS/anti-BRS algebra is presented which is used to understand the relationship between covariant anomalies in different approaches.