A Generalization Of The Horizontality Condition In The Superfield Approach To Nilpotent Symmetries For QED With Complex Scalar Fields

TL;DR

This paper generalizes the superfield approach to BRST symmetry in QED with complex scalar fields, providing a unified framework to derive nilpotent symmetries using a gauge-invariant restriction on a supermanifold.

Contribution

It introduces a generalized horizontality condition within the augmented superfield formalism for deriving BRST symmetries in an interacting U(1) gauge theory with scalar fields.

Findings

Derived (anti-)BRST transformations for all fields in the theory.

Unified framework connecting horizontality condition and gauge-invariant restrictions.

Applicable to 4D interacting gauge theories with scalar matter.

Abstract

We provide a generalization of the horizontality condition of the usual superfield approach to Becchi-Rouet-Stora-Tyutin (BRST) formalism to obtain the nilpotent (anti-)BRST symmetry transformations for all the fields of a four (3 + 1)-dimensional interacting 1-form U(1) gauge theory (QED) within the framework of the augmented superfield formalism. In the above interacting gauge theory, there is an explicit coupling between the 1-form U(1) gauge field and the complex scalar fields. This interacting gauge theory is considered on the (4, 2)-dimensional supermanifold parametrized by the four even spacetime variables x^\mu (with \mu = 0, 1, 2, 3) and a pair of odd Grassmannian variables \theta and \bar\theta. The above (anti-)BRST symmetry transformations are obtained due to the imposition of a gauge (i.e. BRST) invariant restriction on the (4, 2)-dimensional supermanifold. This restriction owes its origin to the (super) covariant derivatives and their intimate connections with the 2-form (super) curvatures. The results obtained, due to the application of the horizontality condition alone, are contained in the results obtained due to the imposition of the gauge (i.e. BRST) invariant restriction on the above supermanifold.