Flux Quantization on M5-branes

TL;DR

This paper explores the global flux-quantization law on M5-branes, revealing its non-abelian cohomological nature and implications for solitons in M-theory.

Contribution

It demonstrates that M5-brane flux quantization is governed by a non-abelian cohomology theory, extending the understanding of flux quantization in M-theory.

Findings

Flux quantization law is in non-abelian cohomology.

Derivation of worldvolume 3-flux via super-embeddings.

Implications for Skyrmion-like and anyonic solitons.

Abstract

We highlight the need for global completion of the field content in the M5-brane sigma-model analogous to Dirac's charge/flux quantization, and we point out that the superspace Bianchi identities on the worldvolume and on its ambient supergravity background constrain the M5's flux-quantization law to be in a non-abelian cohomology theory rationally equivalent to a twisted form of co-Homotopy. In order to clearly bring out this subtle point we give a streamlined re-derivation of the worldvolume 3-flux via M5 "super-embeddings". Finally, assuming the flux-quantization law to actually be in co-Homotopy ("Hypothesis H") we show how this implies Skyrmion-like solitons on general M5-worldvolumes and (abelian) anyonic solitons on the boundaries of "open M5-branes" in heterotic M-theory.