BRST and Superfield Formalism—A Review

• Main Authors: Loriano Bonora, Rudra Prakash Malik
• Format: Article
• Language: English
• Published: MDPI AG 2021-08-01
• Series: Universe
• Subjects: gauge invariant theories; BRST and anti-BRST symmetry; superfield formalism; diffeomorphism invariance; consistent gauge anomalies; HS gauge symmetry
• Online Access: https://www.mdpi.com/2218-1997/7/8/280

This article, which is a review with substantial original material, is meant to offer a comprehensive description of the superfield representations of 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>N</mi><mo>=</mo><mn>1</mn></mrow></semantics></math></inline-formula> super-YM theories formulated in the supersymmetric superspace, for the two formalisms go along with each other very well.