Duality between constraints and gauge conditions

TL;DR

This paper reveals a duality in first order gauge theories where gauge conditions can act as symmetry generators, leading to a new BRST charge and a Hodge operator structure in the cohomology complex.

Contribution

It introduces a novel duality framework where gauge conditions serve as local symmetry generators, expanding the understanding of gauge theory structures.

Findings

Gauge conditions can generate new local symmetries.

A second BRST charge can be associated with these symmetries.

The anticommutator of the two BRST charges corresponds to a Hodge operator.

Abstract

It is shown that in the first order gauge theories under some general assumptions gauge conditions can play the role of new local symmetry generators, while the original constraints become gauge fixing terms. It is possible to associate with this new symmetry a second BRST charge and its anticommutator with the original BRST charge is the Hodge operator of the corresponding cohomology complex.