Modified Proca Theory in Arbitrary and Two Dimensions

TL;DR

This paper explores the gauge and BRST symmetries of the modified Proca theory in arbitrary dimensions, highlighting unique features and symmetries that emerge specifically in two-dimensional spacetime.

Contribution

It demonstrates the preservation of gauge and BRST symmetries in arbitrary dimensions and reveals novel discrete duality and (anti-)co-BRST symmetries in 2D Proca theory.

Findings

BRST symmetry holds in all dimensions

Discrete duality symmetries exist in 2D case

(Anti-)co-BRST symmetries are present in 2D theory

Abstract

We demonstrate that the standard Stueckelberg-modified Proca theory (i.e. a massive Abelian 1-form theory) respects the classical gauge and corresponding quantum (anti-)BRST symmetry transformations in any arbitrary dimension of spacetime within the framework of Becchi-Rouet-Stora-Tyutin (BRST) formalism. We further show that the Stueckelberg formalism gets modified in the two (1+1)-dimensions of spacetime due to a couple of discrete duality symmetries in the theory which turn out to be responsible for the existence of the nilpotent (anti-)co-BRST symmetry transformations corresponding to the nilpotent (anti-)BRST symmetry transformations of our theory. These nilpotent symmetries exist together in the modified version of the two (1+1)-dimensional (2D) Proca theory. We provide the mathematical basis for the modification of the Stueckelberg-technique, the existence of the discrete duality as well as the continuous (anti-)co-BRST symmetry transformations in the 2D modified version of Proca theory.