Anomalies from an effective field theory perspective

TL;DR

This paper introduces a novel method using Covariant Derivative Expansion to compute anomalies in gauge theories, allowing for flexible regularization and a unified derivation of various anomalies.

Contribution

It presents an alternative approach to calculate anomalies from the path-integral measure, enabling customization of regularization to target specific currents.

Findings

Unified derivation of covariant, consistent, gravitational, and scale anomalies.

Flexible regularization techniques for anomaly localization.

Enhanced understanding of anomaly calculations in effective field theories.

Abstract

The path-integral measure of a gauge-invariant fermion theory is transformed under the chiral transformation and leads to an elegant derivation of the anomalous chiral Ward-Takahashi identities, as we know from the seminal work of Fujikawa. We present in this work an alternative and illuminating way to calculate the Jacobian in the path-integral measure from the Covariant Derivative Expansion technique used in Effective Field Theory. We present several ways to customize the crucial regularization such that the anomaly is located in the desired current, which is unprecedented within the path integral approach. We are then able to derive, in a transparent and unified way the covariant, consistent, gravitational and scale anomalies.