Higher form symmetries, membranes and flux quantization

TL;DR

The paper investigates higher form symmetries and anomaly cancellation for a bosonic M2-brane on \\mathcal{M}_9 \\times T^2, showing that a consistent HFS requires a background flux organized by a \\mathcal{G}_1^{\\nabla}-gerbe and a 5D inflow term, which together cancel the 't Hooft anomaly. This construction projects to the M2 worldvolume as a flux quantization condition and yields discrete winding and monopole sectors, realized by Wilson-surface operators with a well-defined fusion algebra. In the toroidal compactification, the symmetry is reduced to a direct sum of discrete factors, \\mathbb{G}^{(1)} \cong \bigoplus_{i=1}^2 \\mathbb{Z}_{N,(w)}^{i} \\oplus \\mathbb{Z}_{M,(m)}, and the Wilson surface charges encode the global holonomy of the membrane. The findings provide a mechanism linking gerbe topology, flux quantization, and spectrum discreteness in M-theory contexts, and point toward deeper connections with abelian ABJ-type anomalies when Wess–Zumino terms are included.

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.