One Loop Anomalies and Wess-Zumino Terms for General Gauge Theories

TL;DR

This paper investigates one-loop anomalies and Wess-Zumino terms in general gauge theories using a Pauli-Villars regularization, revealing their dependence on antifields and their cohomological properties.

Contribution

It provides a detailed analysis of antifield dependence in anomalies and Wess-Zumino terms for on-shell gauge theories, extending the understanding of their cohomological structure.

Findings

Antifield dependence in anomalies is cohomologically non trivial for on-shell theories.

The antifield independent part of the WZ term can be expressed via anomalies and gauge transformations.

Complete WZ term can be reconstructed from its antifield independent component.

Abstract

One loop anomalies and their dependence on antifields for general gauge theories are investigated within a Pauli-Villars regularization scheme. For on-shell theories {\it i.e.}, with open algebras or on-shell reducible theories, the antifield dependence is cohomologically non trivial. The associated Wess-Zumino term depends also on antifields. In the classical basis the antifield independent part of the WZ term is expressed in terms of the anomaly and finite gauge transformations by introducing gauge degrees of freedom as the extra dynamical variables. The complete WZ term is reconstructed from the antifield independent part.