Topological aspects of Abelian gauge theory in superfield formulation

TL;DR

This paper explores the topological features of a 2D Abelian gauge theory using superfield formalism, highlighting the geometric interpretation of symmetries and invariants via supermanifold translations.

Contribution

It provides a superfield framework for expressing topological invariants and symmetries of the gauge theory, emphasizing the geometric role of BRST and co-BRST symmetries.

Findings

Lagrangian density and energy momentum tensor relate to superfield translations

Symmetries are expressed via superfield formalism and horizontality conditions

Topological invariants are formulated in the superfield language

Abstract

We discuss some aspects of the topological features of a non-interacting two (1+1)-dimensional Abelian gauge theory in the framework of superfield formalism. This theory is described by a BRST invariant Lagrangian density in the Feynman gauge. We express the local and continuous symmetries, Lagrangian density, topological invariants and symmetric energy momentum tensor of this theory in the language of superfields by exploiting the nilpotent (anti-)BRST- and (anti-)co-BRST symmetries. In particular, the Lagrangian density and symmetric energy momentum tensor of this topological theory turn out to be the sum of terms that geometrically correspond to the translations of some local superfields along the Grassmannian directions of the four (2+2)-dimensional supermanifold. In this interpretation, the (anti-)BRST- and (anti-)co-BRST symmetries, that emerge after the imposition of the (dual) horizontality conditions, play a very important role.