Nilpotent Symmetries of a 4D Model of the Hodge Theory: Augmented (Anti-)Chiral Superfield Formalism

Abstract

We derive the continuous nilpotent symmetries of the four (3 + 1)-dimensional (4D) model of the Hodge theory (i.e. 4D Abelian 2-form gauge theory) by exploiting the beauty and strength of the symmetry invariant restrictions on the (anti-)chiral superfields. The above off-shell nilpotent symmetries are the Becchi-Rouet-Stora-Tyutin (BRST), anti-BRST and (anti-)co-BRST transformations which turn up beautifully due to the (anti-)BRST and (anti-)co-BRST invariant restrictions on the (anti-)chiral superfields that are defined on the (4, 1)-dimensional (anti-)chiral super-submanifolds of the general (4, 2)-dimensional supermanifold on which our ordinary 4D theory is generalized. The latter supermanifold is characterized by the superspace coordinates $Z^M = (x^μ,\, θ,\, \barθ)$ where $x^μ\, (μ= 0, 1, 2, 3 )$ are the bosonic coordinates and a pair of Grassmannian variables $θ$ and $\barθ$ are fermionic in nature as they obey the standard relationships: $θ^2 = {\barθ}^2 = 0,\, θ\,\barθ+ \barθ\,θ= 0$). The derivation of the {\it proper} (anti-)co-BRST symmetries and proof of the absolute anticommutativity property of the conserved (anti-)BRST and (anti-) co-BRST charges are novel results of our present investigation (where only the (anti-)chiral superfields and their super-expansions have been taken into account).