Nilpotent symmetry invariance in the non-Abelian 1-form gauge theory: superfield formalism

TL;DR

This paper uses superfield formalism to show that BRST and anti-BRST symmetries in a 4D non-Abelian gauge theory with Dirac fields can be represented as Grassmannian independence of a super Lagrangian on a (4,2)-dimensional supermanifold.

Contribution

It demonstrates the superfield approach to capturing BRST invariance in a coupled non-Abelian gauge-Dirac field theory on a supermanifold.

Findings

BRST invariance corresponds to Grassmannian independence of the super Lagrangian

Superfield formalism effectively encodes gauge symmetry invariance

The approach clarifies the geometric origin of BRST symmetries in non-Abelian theories

Abstract

We demonstrate that the nilpotent Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry invariance of the Lagrangian density of a four (3 + 1)-dimensional (4D) non-Abelian 1-form gauge theory with Dirac fields can be captured within the framework of the superfield approach to BRST formalism. The above 4D theory, where there is an explicit coupling between the non-Abelian 1-form gauge field and the Dirac fields, is considered on a (4, 2)-dimensional supermanifold, parameterized by the bosonic 4D space-time variables and a pair of Grassmannian variables. We show that the Grassmannian independence of the super Lagrangian density, expressed in terms of the (4, 2)-dimensional superfields, is a clear signature of the presence of the (anti-)BRST invariance in the original 4D theory.