Non-Geometric Magnetic Flux and Crossed Modules

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.