Background independence and the Adler-Bardeen theorem

TL;DR

This paper proves that in certain Yang-Mills gauge theories, gauge anomaly absence can be confirmed at one-loop level by linking it to background independence, formalized through perturbative agreement.

Contribution

It establishes a connection between gauge anomaly cancellation and background independence in renormalizable Yang-Mills theories, extending the understanding of anomaly conditions.

Findings

Gauge anomalies can be checked at one-loop level.

Background independence is formalized via perturbative agreement.

The method applies to theories with a single abelian factor.

Abstract

We prove that for renormalizable Yang-Mills gauge theory with arbitrary compact gauge group (of at most a single abelian factor) and matter coupling, the absence of gauge anomalies can be established at the one-loop level. This proceeds by relating the gauge anomaly to perturbative agreement, which formalizes background independence.