Superfield approach to topological features of non-Abelian gauge theory

TL;DR

This paper explores the topological features of a 2D non-Abelian gauge theory using superfield formalism, revealing geometric interpretations of key physical quantities via BRST symmetries on a supermanifold.

Contribution

It provides a novel geometric interpretation of topological aspects of non-Abelian gauge theory through superfield formalism and (co-)BRST symmetries.

Findings

Geometric interpretation of the Lagrangian and topological invariants.

Connection between superfield translations and (co-)BRST charges.

Insight into topological features via supermanifold translations.

Abstract

We discuss some of the key topological aspects of a two $(1+1)$-dimensional (2D) self-interacting non-Abelian gauge theory (having no interaction with matter fields) in the framework of {\it chiral} superfield formalism. We provide the geometrical interpretation for the Lagrangian density, symmetric energy momentum tensor, topological invariants, etc., by exploiting the {\it on-shell} nilpotent BRST- and co-BRST symmetries that emerge after the application of (dual) horizontality conditions. We show that the above physically interesting quantities geometrically correspond to the translation of some local (but composite) {\it chiral} superfields along one of the two independent Grassmannian directions of a four ($2+2)$-dimensional supermanifold. This translation is generated by the conserved and on-shell nilpotent (co-)BRST charges that are present in the theory.