Abstract
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 N=1 super-YM theories formulated in the supersymmetric superspace, for the two formalisms go along with each other very well.
Highlights
The discovery of the BRST symmetry in gauge field theories, refs. [1,2,3,4], is a fundamental achievement in quantum field theory
The first is its group theoretical nature: performing two gauge transformations one after the other and reversing the order of them does not lead to the same result, but the two different results are related by a group theoretical rule
We consider BRST and anti-BRST together in the superfield formalism but whenever it is more convenient and expedient to use only the BRST symmetry, we focus only on it
Summary
The discovery of the BRST symmetry in gauge field theories, refs. [1,2,3,4], is a fundamental achievement in quantum field theory. The second important property of the BRST transformations is nilpotency itself It is inherited, via the Faddeev–Popov quantization procedure, from the anticommuting nature of the ghost and anti-ghost fields. The BRST symmetry calls for the introduction of the superfield formulation of quantum field theories. A missing subject in this paper, as well as, to the best of our knowledge, in the present literature, is the exploration of the possibility to extend the superfield method to the Batalin–Vilkovisky approach to field theories with local symmetries.
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