New symmetries for Abelian gauge theory in superfield formulation

TL;DR

This paper uncovers new local, covariant symmetries in a 2D Abelian gauge theory using superfield formalism, linking these symmetries to geometrical translation generators on a supermanifold.

Contribution

It introduces novel symmetries in the superfield formulation of 2D Abelian gauge theory and connects them to geometrical translations and Hodge decompositions.

Findings

Discovery of new local, covariant symmetries in 2D Abelian gauge theory.

Identification of Noether charges as translation generators on supermanifold.

Existence of new discrete symmetries in superfield formulation.

Abstract

We show the existence of some new local, covariant and continuous symmetries for the BRST invariant Lagrangian density of a free two ($1 + 1$)-dimensional (2D) Abelian U(1) gauge theory in the framework of superfield formalism. The Noether conserved charges corresponding to the above local continuous symmetries find their geometrical origin as the translation generators along the odd (Grassmannian)- and even (bosonic) directions of the four ($2 + 2)$-dimensional compact supermanifold. Some new discrete symmetries are shown to exist in the superfield formulation. The logical origin for the existence of BRST- and co-BRST symmetries is shown to be encoded in the Hodge decomposed versions (of the 2D fermionic vector fields) that are consistent with the discrete symmetries of the theory.