The relations between generalized fields and superfields formalisms of the Batalin--Vilkovisky method of quantization

TL;DR

This paper explores the connection between generalized fields and superfields formalisms in the Batalin-Vilkovisky quantization method, demonstrating their equivalence in certain theories and providing solutions for supersymmetric Yang-Mills theory.

Contribution

It establishes a link between two formalisms of the BV method and extends solutions to supersymmetric gauge theories using superfields.

Findings

Generalized fields and superfields formalisms can produce similar results for certain theories.

Truncating superfields yields generalized fields formalism results.

Solution of BV master equation for on-shell N=1 supersymmetric Yang-Mills theory using superfields.

Abstract

A general solution of the Batalin-Vilkovisky master equation was formulated in terms of generalized fields. Recently, a superfields approach of obtaining solutions of the Batalin-Vilkovisky master equation is also established. Superfields formalism is usually applied to topological quantum field theories. However, generalized fields method is suitable to find solutions of the Batalin-Vilkovisky master equation either for topological quantum field theories or the usual gauge theories like Yang-Mills theory. We show that by truncating some components of superfields with appropriate actions, generalized fields formalism of the usual gauge theories result. We demonstrate that for some topological quantum field theories and the relativistic particle both of the methods possess the same field contents and yield similar results. Inspired by the observed relations we give the solution of the BV-master equation for on-shell N=1 supersymmetric Yang-Mills theory utilizing superfields.