A generalization of the horizontality condition in the superfield approach to nilpotent symmetries for QED with complex scalar fields

Abstract

We provide a generalization of the horizontality condition of the usual superfield approach to the Becchi–Rouet–Stora–Tyutin (BRST) formalism to obtain the (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 field theory is considered on the (4, 2)-dimensional supermanifold parametrized by the four even spacetime variables xμ (with μ = 0, 1, 2, 3) and a pair of odd Grassmannian variables θ and . The above nilpotent (anti-)BRST symmetry transformations are obtained due to the imposition of a gauge (i.e. BRST) invariant restriction on the appropriate superfields defined on the (4, 2)-dimensional supermanifold. This restriction owes its origin to a pair of (super) covariant derivatives and their intimate connection with the 2-form (super) curvatures. The results obtained, due to the application of the horizontality condition alone, are contained in the results deduced due to the imposition of the above gauge invariant restriction.