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The Eleven-Dimensional Supergravity Equations on Edge Manifolds

The Eleven-Dimensional Supergravity Equations on Edge Manifolds 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 $$\mathbb B^7\times \mathbb S^4$$ B 7 × S 4 with the characteristic degeneracy at the boundary of an edge system, associated with the fibration with fiber $$\mathbb S^4.$$ 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Annales Henri Poincaré Springer Journals

The Eleven-Dimensional Supergravity Equations on Edge Manifolds

Zhu, Xuwen
Annales Henri Poincaré , Volume 19 (8) – May 30, 2018
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Publisher
Springer Journals
Copyright
Copyright © 2018 by Springer International Publishing AG, part of Springer Nature
Subject
Physics; Theoretical, Mathematical and Computational Physics; Dynamical Systems and Ergodic Theory; Quantum Physics; Mathematical Methods in Physics; Classical and Quantum Gravitation, Relativity Theory; Elementary Particles, Quantum Field Theory
ISSN
1424-0637
eISSN
1424-0661
DOI
10.1007/s00023-018-0689-z
Publisher site
See Article on Publisher Site

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 $$\mathbb B^7\times \mathbb S^4$$ B 7 × S 4 with the characteristic degeneracy at the boundary of an edge system, associated with the fibration with fiber $$\mathbb S^4.$$ 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.

Journal

Annales Henri Poincaré – Springer Journals

Published: May 30, 2018

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