# Nilpotent symmetry invariance in the superfield formulation: the (non-)Abelian 1-form gauge theories

## TL;DR

This paper uses superfield formalism to geometrically interpret the nilpotent BRST and anti-BRST symmetries in 4D (non-)Abelian gauge theories, simplifying their understanding and clarifying subtle points.

## Contribution

It provides a geometric interpretation of BRST symmetries in superfield formalism for 4D gauge theories, enhancing conceptual clarity.

## Key findings

- Geometrical interpretation of nilpotent symmetries
- Simplification of symmetry invariance understanding
- Clarification of subtle points in gauge theories

## Abstract

We capture the off-shell as well as the on-shell nilpotent Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry invariance of the Lagrangian densities of the four (3 + 1)-dimensional (4D) (non-)Abelian 1-form gauge theories within the framework of the superfield formalism. In particular, we provide the geometrical interpretations for (i) the above nilpotent symmetry invariance, and (ii) the above Lagrangian densities, in the language of the specific quantities defined in the domain of the above superfield formalism. Some of the subtle points, connected with the 4D (non-)Abelian 1-form gauge theories, are clarified within the framework of the above superfield formalism where the 4D ordinary gauge theories are considered on the (4, 2)-dimensional supermanifold parametrized by the four spacetime coordinates x^\mu (with \mu = 0, 1, 2, 3) and a pair of Grassmannian variables \theta and \bar\theta. One of the key results of our present investigation is a great deal of simplification in the geometrical understanding of the nilpotent (anti-)BRST symmetry invariance.