BRST and superfield formalism. A review

TL;DR

This review comprehensively discusses superfield representations of BRST and anti-BRST algebras, their applications in gauge theories, anomalies, and supersymmetric models, highlighting the formalism's versatility and recent original contributions.

Contribution

It provides a detailed review of superfield formalism for BRST/anti-BRST algebras, including new insights into gerbes, diffeomorphism invariance, and applications to anomalies and super-Yang-Mills theories.

Findings

Superfield formalism effectively describes gauge and diffeomorphism invariance.

Application to anomalies and Wess-Zumino terms is particularly successful.

BRST superfield formalism integrates well with N=1 super-YM theories.

Abstract

This article, which is a review with substantial original material, is meant to offer a comprehensive description of the superfield representations of the BRST and anti-BRST algebras and their applications to some field-theoretic topics. After a review of the superfield formalism for gauge theories we present the same formalism for gerbes and diffeomorphism invariant theories. The application to diffeomorphisms leads, in particular, to a horizontal Riemannian geometry in the superspace. We then illustrate the application to the description of consistent gauge anomalies and Wess-Zumino terms, for which the formalism seems to be particularly tailor-made. The next subject covered is the higher spin YM-like theories and their anomalies. Finally, we show that the BRST superfield formalism applies as well to the N=1 super-YM theories formulated in the supersymmetric superspace, for the two formalisms go along with each other very well.