### The Moduli 3-Stack of the C-Field

#### Posted by Urs Schreiber

We are in the process of finalizing a little article

Domenico Fiorenza, Hisham Sati, U.S., **The $E_8$ moduli 3-stack of the C-field in M-theory**

**Abstract** 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 ordinary 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 field of gravity and the (auxiliary) E8-Yang-Mills 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 (HS02) to formalize Witten’s argument (Wi96) on the nature of the C-field. Finally we give a similarly simple and natural characterization of the moduli 2-stack of boundary C-field configurations and show that it is equivalent to the smooth moduli 2-stack of anomaly free heterotic supergravity field configurations (SSS12).

This may be read as a companion to the article that I mentioned last time, at Multiple M5-branes, String 2-connections, and 7d nonabelian Chern-Simons theory

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A pdf of the article is behind the above link. Any comment you might have would be most welcome.

Posted at February 9, 2012 9:11 AM UTC
## Re: The Moduli 3-Stack of the C-Field

Some typos from section 1:

“such that the B-field and the RR-fields” such AS

“an integral class divisble by 2.” divisible

“using this machninery”

“Only truncations and reductions … sits” sit