The E8 Moduli 3-Stack of the C-Field in M-Theory

Domenico Fiorenza, Hisham Sati, Urs Schreiber

Research output: Contribution to journalArticle

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 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. 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.

Original languageEnglish (US)
Pages (from-to)117-151
Number of pages35
JournalCommunications in Mathematical Physics
Volume333
Issue number1
DOIs
StatePublished - Jan 1 2014

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M-Theory
Modulus
Cocycle
homology
configurations
Configuration
Cohomology
Quantum Effects
supergravity
Groupoid
gravitational fields
Supergravity
Gauge Field
Gravitational Field
Truncation
Anomaly
anomalies
boundary conditions
Boundary conditions
approximation

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

The E8 Moduli 3-Stack of the C-Field in M-Theory. / Fiorenza, Domenico; Sati, Hisham; Schreiber, Urs.

In: Communications in Mathematical Physics, Vol. 333, No. 1, 01.01.2014, p. 117-151.

Research output: Contribution to journalArticle

Fiorenza, Domenico ; Sati, Hisham ; Schreiber, Urs. / The E8 Moduli 3-Stack of the C-Field in M-Theory. In: Communications in Mathematical Physics. 2014 ; Vol. 333, No. 1. pp. 117-151.
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