Cohomological aspects of gauge theories: superfield formalism

Some of the key cohomological features of the two (1+1)-dimensional (2D) free Abelianand 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-shelland off-shell nilpotent (co-)BRST symmetries that emerge after the application of (dual) horizontality conditions on the supermanifold. 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. PACS: 11.10.-z; 11.30.Ph; 02.40.-k; 02.20.+b; 11.15.-q