Refining the anomaly consistency condition

TL;DR

This paper advances the understanding of anomalies in gauge theories by refining the anomaly consistency condition within the extended antifield formalism, providing new insights into BRST cohomology and anomaly constraints.

Contribution

It introduces a refined anomaly consistency condition in the extended antifield formalism, linking BRST cohomological classes' descent and lift properties during renormalization.

Findings

Anomalies are constrained to classes with shorter descent and longer lift during renormalization.

A simple approach to the Adler-Bardeen theorem is proposed, independent of gauge fixing and power counting.

The formalism characterizes local BRST cohomological classes by form degree, ghost number, descent, and lift.

Abstract

In the extended antifield formalism, a quantum BRST differential for anomalous gauge theories is constructed. Local BRST cohomological classes are characterized, besides the form degree and the ghost number, by the length of their descents and of their lifts, and this both in the standard and the extended antifield formalism. It is shown that during the BRST invariant renormalization of a local BRST cohomological class, the anomaly that can appear is constrained to be a local BRST cohomological class with a shorter descent and a longer lift than the given class. As an application of both results, a simple approach to the Adler-Bardeen theorem for the non abelian gauge anomaly is proposed. It applies independently of the gauge fixing, of power counting restrictions and does not rely on the use of the Callan-Symanzik equation.