The E8 moduli 3-stack of the C-field in M-theory

Understand

The higher gauge field in 11-dimensional supergravity -- the C-field -- is constrained by quantum effects to be a cocycle in some twisted version of differential cohomology.

• We argue that it should indeed be a cocycle in a certain twisted nonabelian differential cohomology.
• We give a simple and natural characterization of the full smooth moduli 3-stack of configurations of the C-field, the gravitational field/background, and the (auxiliary) E8-field.
• We show that the truncation of this moduli 3-stack to a bare 1-groupoid of field configurations reproduces the differential integral Wu structures that Hopkins-Singer had shown to formalize Witten's argument on the nature of the C-field.