The M-theory 3-form and E8 gauge theory

TL;DR

This paper formulates the M-theory 3-form potential in topologically complex settings, relating it to E8 gauge theory and Chern-Simons forms, with implications for flux quantization, anomalies, and heterotic M-theory.

Contribution

It provides a precise mathematical framework for the M-theory 3-form, connecting it to E8 gauge fields and clarifying several physical and topological aspects of M-theory.

Findings

Formulation of the 3-form in topologically nontrivial contexts

Identification of the Chern-Simons term as a cubic refinement

Clarification of Witten's global anomaly and flux quantization

Abstract

We give a precise formulation of the M-theory 3-form potential C in a fashion applicable to topologically nontrivial situations. In our model the 3-form is related to the Chern-Simons form of an E8 gauge field. This leads to a precise version of the Chern-Simons interaction of 11-dimensional supergravity on manifolds with and without boundary. As an application of the formalism we give a formula for the electric C-field charge, as an integral cohomology class, induced by self-interactions of the 3-form and by gravity. As further applications, we identify the M-theory Chern-Simons term as a cubic refinement of a trilinear form, we clarify the physical nature of Witten's global anomaly for 5-brane partition functions, we clarify the relation of M-theory flux quantization to K-theoretic quantization of RR charge, and we indicate how the formalism can be applied to heterotic M-theory.