An Alternative To The Horizontality Condition In Superfield Approach To BRST Symmetries

TL;DR

This paper introduces an alternative gauge-invariant restriction on a supermanifold to derive nilpotent (anti-)BRST symmetry transformations in a 4D non-Abelian gauge theory, replacing the traditional horizontality condition.

Contribution

It proposes a new gauge-invariant restriction method within the superfield approach to derive BRST symmetries, offering an alternative to the conventional horizontality condition.

Findings

Derived BRST transformations using the new restriction.

Established equivalence and differences with the traditional horizontality condition.

Applied the method to an interacting 4D non-Abelian gauge theory with Dirac fields.

Abstract

We provide an alternative to the gauge covariant horizontality condition which is responsible for the derivation of the nilpotent (anti-)BRST symmetry transformations for the gauge and (anti-)ghost fields of a (3 + 1)-dimensional (4D) interacting 1-form non-Abelian gauge theory in the framework of the usual superfield approach to Becchi-Rouet-Stora-Tyutin (BRST) formalism. The above covariant horizontality condition is replaced by a gauge invariant restriction on the (4, 2)-dimensional supermanifold, parameterized by a set of four spacetime coordinates x^\mu (\mu = 0, 1, 2, 3) and a pair of Grassmannian variables \theta and \bar\theta. The latter condition enables us to derive the nilpotent (anti-)BRST symmetry transformations for all the fields of an interacting 4D 1-form non-Abelian gauge theory where there is an explicit coupling between the gauge field and the Dirac fields. The key differences and striking similarities between the above two conditions are pointed out clearly.