Higher form symmetries, membranes and flux quantization

TL;DR

This paper explores higher form symmetries in M2-brane theories on compactified spaces, linking anomaly cancellation to flux quantization via gerbe structures, and introduces topological operators that encode these symmetries.

Contribution

It establishes a connection between anomaly cancellation, flux quantization, and gerbe structures in M2-brane theories, providing a detailed analysis of the associated topological operators.

Findings

Higher form symmetries are characterized in M2-brane theories.

Flux quantization conditions are related to gerbe structures.

Topological operators realize discrete symmetries and have well-defined algebra.

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.