Higher form symmetries, membranes and flux quantization

Abstract

Higher Forms Symmetries (HFS) of a closed bosonic M2-brane theory formulated on a compactified target space ${\mathcal{M}}_9\times T^2$ are obtained. We show that the cancellation of the 't Hooft anomaly present in the theory is related to a 3-form flux with ${\mathcal{G}}_1^{\nabla }$-gerbe structure associated to the world-volume flux quantization condition. A Wilson surface is naturally introduced on the topological operator that characterize the holonomy of the M2-brane. The projection of the flux quantization condition inherited from the gerbe structure onto the spatial part of the worldvolume, leads to a flux quantization on the M2-brane. The topological operators realise discrete symmetries associated with the winding and the flux/monopole condition. The algebra of operators is well defined.

Latex, 21 pages, Writing has been improved in order to clarify the content, keeping the results unchanged. Typos have been corrected