Comments on the dual-BRST symmetry

TL;DR

This paper clarifies the independence of dual-BRST and BRST symmetries in gauge theories using differential geometry, resolving recent controversies by emphasizing their mathematical distinction as cohomological operators.

Contribution

It demonstrates that dual-BRST and BRST symmetries are independent, grounded in the mathematics of differential geometry and Hodge theory, countering claims of their dependence.

Findings

BRST and co-BRST are independent symmetries.

They correspond to exterior and co-exterior derivatives.

The independence is analogous to de Rham cohomological operators.

Abstract

In view of a raging controversy on the topic of dual-Becchi-Rouet-Stora-Tyutin (dual-BRST/co-BRST) and anti-co-BRST symmetry transformations in the context of four (3+1)-dimensional (4D) Abelian 2-form and 2D (non-)Abelian 1-form gauge theories, we attempt, in our present short note, to settle the dust by taking the help of mathematics of differential geometry, connected with the Hodge theory, which was the original motivation for the nomenclature of "dual-BRST symmetry" in our earlier set of works. It has been claimed, in a recent set of papers, that the co-BRST symmetries are not independent of the BRST symmetries. We show that the BRST and co-BRST symmetries are independent symmetries in the same fashion as the exterior and co-exterior derivatives are independent entities belonging to the set of de Rham cohomological operators of differential geometry.