Axial anomaly in the presence of arbitrary spinor interactions

TL;DR

This paper generalizes the axial anomaly calculation for Dirac fermions to include arbitrary spinor interactions, establishing conditions for anomaly finiteness using Pauli-Villars regularization.

Contribution

It introduces a framework for analyzing axial anomalies with arbitrary Clifford-valued external fields, extending previous Yang-Mills interaction results.

Findings

Derived conditions for anomaly finiteness.

Computed the axial anomaly in the generalized setting.

Extended known anomaly results to broader interactions.

Abstract

We consider N Dirac fermions on a 4-dimensional Euclidean space with a quadratic interaction given by arbitrary external Clifford-valued fields. The divergence of the axial current satisfies on the classical level a relation that is violated after quantization. Using the Pauli-Villars method to regularize the fields, we find the conditions that guarantee the finiteness of the anomaly. We also find this anomaly. Our result generalizes the well-known computation of axial anomaly of Dirac fermions interacting with an external Yang-Mills field.