Cohomotopy and flux quantization in $M$-theory

TL;DR

This paper explores the mathematical structure of flux quantization in M-theory using cohomotopy theory, establishing conditions for the well-definedness of the Chern--Simons term without requiring an E8 gauge field.

Contribution

It identifies key k-invariants in the Postnikov tower of the 4-sphere and applies obstruction theory under Hypothesis H to prove flux quantization consistency in M-theory.

Findings

Chern--Simons term is well-defined under certain topological conditions.

No need for E8 gauge field in the flux quantization framework.

Advances understanding of M-theory's mathematical foundations.

Abstract

We identify some of the $k$-invariants for the Postnikov tower of the stable and unstable 4-sphere. Assuming the stable Hypothesis H of Fiorenza--Sati--Schreiber, we use the resulting obstruction theory to prove that the Chern--Simons term in the effective action of M-theory is well defined. In particular, we do not assume the presence of an $E_8$-gauge field.