A New Approach to Axial Vector Model Calculations

TL;DR

This paper introduces a novel method for calculating the one-loop effective action in axial vector models, utilizing an auxiliary gauge connection and a new worldline path integral representation to improve analysis and computation.

Contribution

It presents a new approach that rewrites the effective action in terms of an auxiliary gauge connection and derives a worldline path integral avoiding traditional complexities.

Findings

Derived a new worldline path integral representation.

Analyzed anomalous and non-anomalous content using De Witt expansion.

Provided a simplified framework for axial vector model calculations.

Abstract

We consider the one-loop effective action due to a spinor loop coupled to an abelian vector and axial vector field background. After rewriting this effective action in terms of an auxiliary non-abelian gauge connection, we use the De Witt expansion to analyze both its anomalous and non-anomalous content. The same transformation allows us to obtain a novel worldline path integral representation for this effective action which avoids the usual separation into the real and imaginary parts of the Euclidean effective action, as well as the introduction of auxiliary dimensions.