Anomaly of a gauge theory under rescaling of the fields

TL;DR

This paper investigates the field rescaling anomaly in quantum gauge theories, showing its dependence on the spin term and providing a method to extract it directly from the effective action, applicable to various gauge theories.

Contribution

It introduces a new approach to determine the field rescaling anomaly without using Fujikawa's method, emphasizing the role of the spin term in the action.

Findings

The anomaly depends on the spin term in the action.

The anomaly can be extracted from the spin contribution to the one-loop effective action.

Results agree with previous Fujikawa-based calculations for supersymmetric theories.

Abstract

We determine the anomaly associated to an arbitrary scaling of the fields in a quantum gauge theory without making use of the Fujikawa method. We show that this anomaly is dependent on the spin term present in the action and at one loop can be directly extracted from the spin contribution to the one loop effective action. Our results can be readily applied to any gauge theory, supersymmetric or not and agree with previous determination for supersymmetric gauge theories based on the Fujikawa method.