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

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 field theory is considered on the six (4, 2)-dimensional supermanifold parametrized by the four even spacetime variables x µ (with µ = 0, 1, 2, 3) and a couple of odd Grassmannian variables θ and ¯ θ. The above (anti-)BRST symmetry transformations are obtained due to the imposition of a gauge (i.e. BRST) invariant restriction on the six (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.