Ward identities and gauge independence in general chiral gauge theories

TL;DR

This paper uses the Batalin-Vilkovisky formalism to analyze gauge identities and dependence in potentially anomalous chiral gauge theories, demonstrating gauge invariance implies gauge independence and perturbative unitarity.

Contribution

It proves that gauge invariance ensures gauge independence in anomalous theories that are anomaly-free due to the Adler-Bardeen theorem, and shows how renormalized functionals relate under canonical transformations.

Findings

Gauge invariance implies gauge independence and unitarity.

Renormalized functionals can be related via canonical transformations.

Beta functions may depend on gauge-fixing parameters without affecting physical quantities.

Abstract

Using the Batalin-Vilkovisky formalism, we study the Ward identities and the equations of gauge dependence in potentially anomalous general gauge theories, renormalizable or not. A crucial new term, absent in manifestly nonanomalous theories, is responsible for interesting effects. We prove that gauge invariance always implies gauge independence, which in turn ensures perturbative unitarity. Precisely, we consider potentially anomalous theories that are actually free of gauge anomalies thanks to the Adler-Bardeen theorem. We show that when we make a canonical transformation on the tree-level action, it is always possible to re-renormalize the divergences and re-fine-tune the finite local counterterms, so that the renormalized $\Gamma $ functional of the transformed theory is also free of gauge anomalies, and is related to the renormalized $\Gamma $ functional of the starting theory by a canonical transformation. An unexpected consequence of our results is that the beta functions of the couplings may depend on the gauge-fixing parameters, although the physical quantities remain gauge independent. We discuss nontrivial checks of high-order calculations based on gauge independence and determine how powerful they are.