  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 $Z^M =
(x^\mu,\, \theta,\, \bar\theta)$ where $x^\mu\, (\mu = 0, 1, 2, 3 )$ are the
bosonic coordinates and a pair of Grassmannian variables $\theta$ and
$\bar\theta$ are fermionic in nature as they obey the standard relationships:
$\theta^2 = {\bar\theta}^2 = 0,\, \theta\,\bar\theta + \bar\theta\,\theta =
0$). 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).
