### 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) 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.

Original language | English (US) |
---|---|

Pages (from-to) | 117-151 |

Number of pages | 35 |

Journal | Communications in Mathematical Physics |

Volume | 333 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 2014 |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

_{8}Moduli 3-Stack of the C-Field in M-Theory.

*Communications in Mathematical Physics*,

*333*(1), 117-151. https://doi.org/10.1007/s00220-014-2228-1

**The E _{8} Moduli 3-Stack of the C-Field in M-Theory.** / Fiorenza, Domenico; Sati, Hisham; Schreiber, Urs.

Research output: Contribution to journal › Article

_{8}Moduli 3-Stack of the C-Field in M-Theory',

*Communications in Mathematical Physics*, vol. 333, no. 1, pp. 117-151. https://doi.org/10.1007/s00220-014-2228-1

_{8}Moduli 3-Stack of the C-Field in M-Theory. Communications in Mathematical Physics. 2014 Jan 1;333(1):117-151. https://doi.org/10.1007/s00220-014-2228-1

}

TY - JOUR

T1 - The E8 Moduli 3-Stack of the C-Field in M-Theory

AU - Fiorenza, Domenico

AU - Sati, Hisham

AU - Schreiber, Urs

PY - 2014/1/1

Y1 - 2014/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84925461000&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84925461000&partnerID=8YFLogxK

U2 - 10.1007/s00220-014-2228-1

DO - 10.1007/s00220-014-2228-1

M3 - Article

AN - SCOPUS:84925461000

VL - 333

SP - 117

EP - 151

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 1

ER -