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The Eleven-Dimensional Supergravity Equations on Edge Manifolds

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Abstract

We study the 11-dimensional supergravity equations which describe a low-energy approximation to string theories and are related to M-theory under the AdS/CFT correspondence. These equations take the form of a nonlinear differential system, on \(\mathbb B^7\times \mathbb S^4\) with the characteristic degeneracy at the boundary of an edge system, associated with the fibration with fiber \(\mathbb S^4.\) We compute the indicial roots of the linearized system from the Hodge decomposition of the 4-sphere following the work of Kantor, and then using the edge calculus and scattering theory, we prove that the moduli space of solutions, near the Freund–Rubin states, is parametrized by three pairs of data on the bounding 6-sphere.

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Authors and Affiliations

  1. Department of Mathematics, Stanford University, Stanford, CA, 94305, USA

    Xuwen Zhu

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  1. Xuwen Zhu
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Correspondence to Xuwen Zhu.

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Communicated by Boris Pioline.

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Zhu, X. The Eleven-Dimensional Supergravity Equations on Edge Manifolds. Ann. Henri Poincaré 19, 2347–2400 (2018). https://doi.org/10.1007/s00023-018-0689-z

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  • DOI: https://doi.org/10.1007/s00023-018-0689-z

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