The power of the anomaly consistency condition for the Master Ward Identity: Conservation of the non-Abelian gauge current

TL;DR

This paper demonstrates that the consistency condition for the Master Ward Identity effectively excludes all potential anomalies in non-Abelian gauge theories, ensuring gauge current conservation beyond perturbative anomalies.

Contribution

It extends the Master Ward Identity framework to non-Abelian gauge theories and proves anomaly exclusion using the consistency condition.

Findings

All potential anomalies are excluded by the consistency condition.

Gauge current conservation holds up to removable terms.

The approach strengthens the theoretical foundation of gauge symmetry in quantum field theory.

Abstract

Extending local gauge tansformations in a suitable way to Faddeev-Popov ghost fields, one obtains a symmetry of the total action, i.e., the Yang-Mills action plus a gauge fixing term (in a lambda-gauge) plus the ghost action. The anomalous Master Ward Identity (for this action and this extended, local gauge transformation) states that the pertinent Noether current -- the interacting ``gauge current'' -- is conserved up to anomalies. It is proved that, apart from terms being easily removable (by finite renormalization), all possible anomalies are excluded by the consistency condition for the anomaly of the Master Ward Identity, recently derived in refenrence [8].