LAUSR

Abstract We derive the continuous nilpotent symmetries of the four ( 3 + 1 ) -dimensional (4 D ) model of the Hodge theory (i.e. 4 D 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 4 D theory is generalized. The latter supermanifold is characterized by the superspace coordinates Z M = ( x μ , θ , θ ) where x μ ( μ = 0 , 1 , 2 , 3 ) are the bosonic coordinates and a pair of Grassmannian variables θ and θ are fermionic in nature as they obey the standard relationships: θ 2 = θ 2 = 0 , θ θ + θ θ = 0 ). The derivation of the 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).