Cohomological aspects of gauge theories: superfield formalism

TL;DR

This paper explores the cohomological features of 2D Abelian and non-Abelian gauge theories using superfield formalism, revealing new symmetries and geometric insights into their topological nature.

Contribution

It introduces a superfield formulation that derives new symmetries and offers geometric interpretations of topological quantities in 2D gauge theories.

Findings

Derived new symmetries for the Lagrangian and energy-momentum tensor.

Provided geometric interpretations of topologically interesting quantities.

Demonstrated the role of (anti-)chiral superfields in symmetry derivation.

Abstract

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.