Refined chiral Slavnov-Taylor identities: Renormalization and Local Physics

TL;DR

This paper investigates the quantization of chiral QED using an extended Slavnov-Taylor identity that includes anomalies, revealing how the introduction of a doublet affects the cohomology of the model and its implications for renormalization.

Contribution

It demonstrates that the extended Slavnov-Taylor identity modifies the cohomology classes of the linearized operator, providing a counterexample to the invariance of cohomology under doublet introduction.

Findings

Extended ST identity incorporates the Adler-Bardeen anomaly.

Cohomology classes are altered by the doublet in the extended ST framework.

Counterexample showing cohomology modification due to non-commuting counting operator.

Abstract

We study the quantization of chiral QED by means of an extended Slavnov-Taylor (ST) identity under which an external source and the ghost field form a doublet. This ST identity incorporates the Adler-Bardeen anomaly. We prove that the cohomology classes of the extended classical linearized ST operator ${\cal S}'_0$ are modified with respect to the ones of the classical BRST differential in the FP neutral sector (physical observables). This provides a counterexample showing that the introduction of a doublet can modify the cohomology of the model, as a consequence of the fact that the counting operator for the doublet does not commute with ${\cal S}'_0$.