  Some of the key cohomological features of the two $(1+1)$-dimensional (2D)
free Abelian- and self-interacting non-Abelian gauge theories (having no
interaction with matter fields) are briefly discussed first in the language of
symmetry properties of the Lagrangian densities and the same issues are
subsequently addressed in the framework of superfield formulation on the four
($2 + 2)$-dimensional supermanifold. Special emphasis is laid on the on-shell-
and off-shell nilpotent (co-)BRST symmetries that emerge after the application
of (dual) horizontality conditions on the supermanifold. The (anti-)chiral
superfields play a very decisive role in the derivation of the on-shell
nilpotent symmetries. The study of the present superfield formulation leads to
the derivation of some new symmetries for the Lagrangian density and the
symmetric energy-momentum tensor. The topological nature of the above theories
is captured in the framework of superfield formulation and the geometrical
interpretations are provided for some of the topologically interesting
quantities.
