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arXiv · 1202.2455

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

Domenico Fiorenza·Hisham Sati·Urs Schreiber
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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 Horava-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.

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Domenico Fiorenza, Hisham Sati, Urs Schreiber. 2012-02-11. The E8 moduli 3-stack of the C-field in M-theory. https://doi.org/10.1007/s00220-014-2228-1

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