Dual-BRST symmetry: 6D Abelian 3-form gauge theory

TL;DR

This paper explores the discovery of novel off-shell nilpotent (anti-)dual-BRST symmetries in a 6D Abelian 3-form gauge theory, revealing a rich algebraic structure akin to de Rham cohomology.

Contribution

It introduces the off-shell nilpotent (anti-)dual-BRST symmetries in 6D Abelian 3-form gauge theory and analyzes their algebraic structure and connections.

Findings

Existence of off-shell nilpotent (anti-)dual-BRST symmetries.

Invariance of gauge-fixing term under these symmetries.

Algebraic structure similar to de Rham cohomology.

Abstract

Within the framework of Becchi-Rouet-Stora-Tyutin (BRST) formalism, we demonstrate the existence of the novel off-shell nilpotent (anti-)dual-BRST symmetries in the context of a six (5 + 1)-dimensional (6D) free Abelian 3-form gauge theory. Under these local and continuous symmetry transformations, the total gauge-fixing term of the Lagrangian density remains invariant. This observation should be contrasted with the off-shell nilpotent (anti-)BRST symmetry transformations, under which, the total kinetic term of the theory remains invariant. The anticommutator of the above nilpotent (anti-)BRST and (anti-)dual-BRST transformations leads to the derivation of a bosonic symmetry in the theory. There exists a discrete symmetry transformation in the theory which provides a thread of connection between the nilpotent (anti-)BRST and (anti-)dual-BRST transformations. This theory is endowed with a ghost-scale symmetry, too. We discuss the algebra of these symmetry transformations and show that the structure of the algebra is reminiscent of the algebra of de Rham cohomological operators of differential geometry.