Anyons on M5-Probes of Seifert 3-Orbifolds via Flux Quantization

TL;DR

This paper establishes a rigorous route to abelian anyonic states in M-theory by invoking flux quantization as a global completion of higher gauge theories on M5-branes wrapped on Seifert orbifolds. Using equivariant twistorial Cohomotopy, it shows that the self-dual tensor sector and background C-field induce nontrivial solitonic sectors, which reduce to plain $2$-Cohomotopy on the 1+2D fixed locus, thereby yielding abelian anyons. The analysis extends to $\Z_2$-equivariant orbifold settings, where the fixed locus reduces to $S^2$, providing a concrete topological framework for anyonic statistics in the M5 context and clarifying how twistorial quantization encodes subtle M-theory topological effects. Collectively, these results offer a first-principles mechanism for topological order within M-theory and highlight flux quantization as a crucial step toward a nonperturbative completion of 11D supergravity with potential holographic applications to strongly correlated quantum systems.

Abstract

We observe that there is a rigorous derivation of (abelian) anyonic quantum states, hence of "topological order", on the 1+2-dimensional fixed locus of M5-probes wrapped over a trivially Seifert-fibered 3-orbifold singularity. Similar statements have previously been conjectured by appeal to the unknown dynamics of "coincident" M5-branes, but neglecting effects of flux-quantization that, as we highlight, entail anyonic solitons already in the rigorously tractable case of single M5-brane probes. This is possible after globally completing the "self-dual" tensor field on probe M5-branes by flux quantization in the non-abelian cohomology theory called equivariant twistorial Cohomotopy, which is admissible by recent results.