Gauge anomaly cancellation in chiral gauge theories

TL;DR

This paper demonstrates that gauge anomalies in chiral gauge theories have null expectation values in the vacuum and do not affect physical correlators, indicating a form of anomaly cancellation.

Contribution

It introduces a path integral approach showing gauge anomaly expectation values vanish in the vacuum and argues that the mechanism cannot cancel the chiral anomaly, clarifying anomaly behavior.

Findings

Gauge anomaly expectation value is null in the vacuum.

Gauge anomaly insertion in correlators yields null results.

Mechanism cannot cancel the chiral anomaly.

Abstract

We consider chiral fermions interacting minimally with abelian and non-abelian gauge fields. Using a path integral approach and exploring the consequences of a mechanism of symmetry restoration, we show that the gauge anomaly has null expectation value in the vacuum for both cases (abelian and non-abelian). We argue that the same mechanism has no possibility to cancel the chiral anomaly, what eliminates competition between chiral and gauge symmetry at full quantum level. We also show that the insertion of the gauge anomaly in arbitrary gauge invariant correlators gives a null result, which points towards anomaly cancellation in the subspace of physical state vectors.