Communications in Mathematical Physics

, Volume 333, Issue 1, pp 117–151 | Cite as

The E 8 Moduli 3-Stack of the C-Field in M-Theory

  • Domenico Fiorenza
  • Hisham Sati
  • Urs SchreiberEmail author


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) E 8-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. 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 moduli 2-stack of anomaly free heterotic supergravity field configurations. Finally, we show how to naturally encode the Hořava–Witten boundary condition on the level of moduli 3-stacks, and refine it from a condition on 3-forms to a condition on the corresponding full differential cocycles.


Gauge Transformation Simons Theory Canonical Morphism High Gauge Bundle Gerbe 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Dipartimento di MatematicaSapienza - Università di RomaRomaItaly
  2. 2.Department of MathematicsUniversity of PittsburghPittsburghUSA
  3. 3.Department of MathematicsUniversity of NijmegenNijmegenThe Netherlands

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