Novel symmetries in the modified version of two dimensional Proca theory

TL;DR

This paper explores the extended symmetry structure of a modified 2D Proca gauge theory, revealing its connection to Hodge theory and differential geometry through novel (anti-)co-BRST symmetries.

Contribution

It introduces on-shell nilpotent (anti-)co-BRST symmetries in the 2D Proca theory and links these symmetries to Hodge theory, providing a new field-theoretic example.

Findings

The theory exhibits unique bosonic symmetry from BRST and co-BRST anticommutators.

The symmetries realize de Rham cohomological operators physically.

The model demonstrates the Hodge duality operation in a gauge theory context.

Abstract

By exploiting Stueckelberg's approach, we obtain a gauge theory for the two (1+1)-dimensional (2D) Proca theory and demonstrate that this theory is endowed with, in addition to the usual Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetries, the on-shell nilpotent (anti-)co-BRST symmetries, under which the total gauge-fixing term remains invariant. The anticommutator of the BRST and co-BRST (as well as anti-BRST and anti-co-BRST) symmetries define a unique bosonic symmetry in the theory, under which the ghost part of the Lagrangian density remains invariant. To establish connections of the above symmetries with the Hodge theory, we invoke a pseudo-scalar field in the theory. Ultimately, we demonstrate that the full theory provides a field theoretic example for the Hodge theory where the continuous symmetry transformations provide a physical realization of the de Rham cohomological operators and discrete symmetries of the theory lead to the physical realization of the Hodge duality operation of differential geometry. We also mention the physical implications and utility of our present investigation.