Local BRST cohomology in gauge theories

TL;DR

This paper reviews the recent solutions to the BRST cohomology problem in gauge theories, including anomaly cancellation and counterterm classification, using algebraic methods applicable across various gauge models.

Contribution

It provides a comprehensive, self-contained review of the algebraic techniques for computing BRST cohomology and their applications to gauge theory anomalies and renormalization.

Findings

Solution of the Wess-Zumino anomaly condition

Classification of counterterms in gauge theories

Application of cohomology to conservation laws

Abstract

The general solution of the anomaly consistency condition (Wess-Zumino equation) has been found recently for Yang-Mills gauge theory. The general form of the counterterms arising in the renormalization of gauge invariant operators (Kluberg-Stern and Zuber conjecture) and in gauge theories of the Yang-Mills type with non power counting renormalizable couplings has also been worked out in any number of spacetime dimensions. This Physics Report is devoted to reviewing in a self-contained manner these results and their proofs. This involves computing cohomology groups of the differential introduced by Becchi, Rouet, Stora and Tyutin, with the sources of the BRST variations of the fields ("antifields") included in the problem. Applications of this computation to other physical questions (classical deformations of the action, conservation laws) are also considered. The general algebraic techniques developed in the Report can be applied to other gauge theories, for which relevant references are given.