Superfield Approach to (Non-)local Symmetries for One-Form Abelian Gauge Theory

TL;DR

This paper uses superfield formalism to derive and interpret local and non-local BRST and dual-BRST symmetries in four-dimensional Abelian gauge theory, providing geometric insights into their origins.

Contribution

It introduces a superfield approach to systematically derive and interpret both local and non-local BRST symmetries in 4D Abelian gauge theory.

Findings

Derived local and non-local BRST and dual-BRST transformations.

Provided geometric interpretation of (dual-)BRST charges.

Connected superfield translations to symmetry transformations.

Abstract

We exploit the geometrical superfield formalism to derive the local, covariant and continuous Becchi-Rouet-Stora-Tyutin (BRST) symmetry transformations and the non-local, non-covariant and continuous dual-BRST symmetry transformations for the free Abelian one-form gauge theory in four $(3 + 1)$-dimensions (4D) of spacetime. Our discussion is carried out in the framework of BRST invariant Lagrangian density for the above 4D theory in the Feynman gauge. The geometrical origin and interpretation for the (dual-)BRST charges (and the transformations they generate) are provided in the language of translations of some superfields along the Grassmannian directions of the six ($ 4 + 2)$-dimensional supermanifold parametrized by the four spacetime and two Grassmannian variables.