Augmented Superfield Approach to Nilpotent Symmetries in the Modified Version of 2D Proca Theory

TL;DR

This paper develops a comprehensive superfield formalism to derive and analyze nilpotent BRST, anti-BRST, and (anti-)co-BRST symmetries in a modified 2D Proca theory, revealing novel insights and its connection to Hodge theory.

Contribution

It introduces an augmented superfield approach to systematically derive all nilpotent symmetries in the modified 2D Proca theory, highlighting new observations in superfield BRST formalism.

Findings

Complete set of off-shell nilpotent symmetries derived

Novel observations in superfield approach identified

The theory models Hodge theory through charge algebra

Abstract

We derive the complete set of off-shell nilpotent and absolutely anticommuting Becchi-Rouet-Stora-Tyutin (BRST), anti-BRST and (anti-)co-BRST symmetry transformations for all the fields of the modified version of two (1+1)-dimensional (2D) Proca theory by exploiting the "augmented" superfield formalism where the (dual-)horizontality conditions and (dual-)gauge-invariant restrictions are exploited together. We capture the (anti-)BRST and (anti-)co-BRST invariance of the Lagrangian density in the language of superfield formalism. We also express the nilpotency and absolute anticommutativity of the (anti-)BRST and (anti-)co-BRST charges within the framework of augmented superfield formalism. This exercise leads to some novel observations which have, hitherto, not been pointed out in the literature within the framework of superfield approach to BRST formalism. For the sake of completeness, we also mention, very briefly, a unique bosonic symmetry, the ghost-scale symmetry and discrete symmetries of the theory and show that the algebra of conserved charges captures the cohomological aspects of differential geometry. Thus, our present modified 2D Proca theory is a model for the Hodge Theory.