BRST, anti-BRST and gerbes

TL;DR

This paper explores the BRST and anti-BRST symmetries of Abelian 2-form gauge fields in 4D, revealing a consistency condition akin to gerbes, which links gauge theory to higher geometric structures.

Contribution

It establishes a connection between BRST symmetry conditions and gerbes, extending gauge theory understanding to higher-form fields and geometric frameworks.

Findings

Imposition of a Curci-Ferrari-like condition for BRST symmetry closure

Identification of the gauge theory as based on gerbes

Formulation of symmetry transformations for 1- and 2-gerbes

Abstract

We discuss BRST and anti--BRST transformations for an Abelian antisymmetric gauge field in 4D and find that, in order for them to anticommute, we have to impose a condition on the auxiliary fields. This condition is similar to the Curci-Ferrari condition for the 4D non--Abelian 1-form gauge theories and represents a consistency requirement. We interpret it as a signal that our Abelian 2-form gauge field theory is based on gerbes. To support this interpretation we discuss, in particular, the case of the 1-gerbe for our present field theory and write the relevant equations and symmetry transformations for 2-gerbes.