Non-Geometric Magnetic Flux and Crossed Modules

TL;DR

This paper links the BRST operator in twisted N=4 Yang-Mills theory to non-Abelian gerbes, introducing non-geometric magnetic fluxes classified by cohomology, advancing understanding of non-perturbative backgrounds and non-local five-brane dynamics.

Contribution

It establishes a novel connection between BRST operators and non-Abelian gerbes, introducing non-geometric magnetic fluxes classified by cohomology.

Findings

Identifies non-geometric magnetic fluxes in Yang-Mills theory

Classifies fluxes using cohomology of non-Abelian gerbes

Links non-Abelian gerbes to non-local five-brane dynamics

Abstract

It is shown that the BRST operator of twisted N=4 Yang-Mills theory in four dimensions is locally the same as the BRST operator of a fully decomposed non-Abelian gerbe. Using locally defined Yang-Mills theories we describe non-perturbative backgrounds that carry a novel magnetic flux. Given by elements of the crossed module G x Aut G, these non-geometric fluxes can be classified in terms of the cohomology class of the underlying non-Abelian gerbe, and generalise the centre ZG valued magnetic flux found by 't Hooft. These results shed light also on the description of non-local dynamics of the chiral five-brane in terms of non-Abelian gerbes.