(Anti-)dual-BRST symmetries: Abelian 2-form gauge theory

TL;DR

This paper establishes (anti-)dual-BRST symmetries for 4D Abelian 2-form gauge theory, revealing their geometric analogies to differential operators and elucidating the algebraic structure of these symmetries.

Contribution

It introduces the (anti-)dual-BRST symmetries for Abelian 2-form gauge theory and explores their geometric and algebraic properties, extending the understanding of gauge symmetries.

Findings

Derived the (anti-)dual-BRST symmetry transformations.

Showed the symmetry algebra mirrors de Rham cohomology.

Identified a bosonic symmetry analogous to the Laplacian.

Abstract

We derive the absolutely anticommuting (anti-)dual-BRST symmetry transformations for the appropriate Lagrangian densities of the (3 + 1)-dimensional (4D) free Abelian 2-form gauge theory, under which, the total gauge-fixing term remains invariant. These symmetry transformations are the analogue of the co-exterior derivative of differential geometry, in the same sense, as the absolutely anticommuting (anti-)BRST symmetry transformations are the analogue of the exterior derivative. A bosonic symmetry transformation is shown to be the analogue of the Laplacian operator. The algebraic structures of these symmetry transformations are derived and they are demonstrated to be the reminiscent of the algebra obeyed by the de Rham cohomological operators of differential geometry.