Higher order cohomological restrictions on anomalies and counterterms

TL;DR

This paper establishes higher order local consistency conditions for one-loop anomalies and counterterms in gauge theories, derived without assuming specific BRST cohomology forms, ensuring their compatibility with the master equation.

Contribution

It introduces a regularization-based method to derive higher order restrictions on anomalies and counterterms without prior assumptions on BRST cohomology.

Findings

First order anomalies are BRST exact when combined with BRST cocycles.

First order counterterms can be extended into local deformations of the master equation.

Anomalies can be deformed into local cocycles of the deformed solution.

Abstract

Using a regularization with the properties of dimensional regularization, higher order local consistency conditions on one loop anomalies and divergent counterterms are given. They are derived without any a priori assumption on the form of the BRST cohomology and can be summarized by the statements that (i) the antibracket involving the first order divergent counterterms, respectively the first order anomaly, with any BRST cocycle is BRST exact, (ii) the first order divergent counterterms can be completed into a local deformation of the solution of the master equation and (iii) the first order anomaly can be deformed into a local cocycle of the deformed solution.