# Modified 2D Proca Theory: Revisited Under BRST and (Anti-)Chiral Superfield Formalisms

## TL;DR

This paper revisits the modified 2D Proca theory using BRST and superfield formalisms, revealing new restrictions and symmetries, and analyzing their mathematical and physical implications.

## Contribution

It introduces a novel superfield approach to analyze BRST symmetries in the modified 2D Proca theory, highlighting unique restrictions different from standard gauge theories.

## Key findings

- Existence of new restrictions in the modified 2D Proca theory.
- Derivation of off-shell nilpotent (anti-)BRST and (anti-)co-BRST charges.
- Insights into the negative kinetic term of the pseudo-scalar field.

## Abstract

Within the framework of Becchi-Rouet-Stora-Tyutin (BRST) approach, we discuss mainly the fermionic (i.e. off-shell nilpotent) (anti-)BRST, (anti-)co-BRST and some discrete dual-symmetries of the appropriate Lagrangian densities for a two (1+1)-dimensional (2D) modified Proca (i.e. a massive Abelian 1-form) theory without any interaction with matter fields. One of the novel observations of our present investigation is the existence of some kinds of restrictions in the case of our present St\"{u}ckelberg-modified version of the 2D Proca theory which is not like the standard Curci-Ferrari (CF)-condition of a non-Abelian 1-form gauge theory. Some kinds of similarities and a few differences between them have been pointed out in our present investigation. To establish the sanctity of the above off-shell nilpotent (anti-)BRST and (anti-)co-BRST symmetries, we derive them by using our newly proposed (anti-)chiral superfield formalism where a few specific and appropriate sets of invariant quantities play a decisive role. We express the (anti-)BRST and (anti-)co-BRST conserved charges in terms of the superfields that are obtained after the applications of (anti-)BRST and (anti-)co-BRST invariant restrictions and prove their off-shell nilpotency and absolute anticommutativity properties, too. Finally, we make some comments on (i) the novelty of our restrictions/obstructions, and (ii) the physics behind the negative kinetic term associated with the pseudo-scalar field of our present theory.