The Eleven-Dimensional Supergravity Equations on Edge Manifolds

The Eleven-Dimensional Supergravity Equations on Edge Manifolds Ann. Henri Poincar´ e Online First c 2018 Springer International Publishing AG, part of Springer Nature Annales Henri Poincar´ e https://doi.org/10.1007/s00023-018-0689-z The Eleven-Dimensional Supergravity Equations on Edge Manifolds Xuwen Zhu Abstract. We study the 11-dimensional supergravity equations which de- scribe a low-energy approximation to string theories and are related to M-theory under the AdS/CFT correspondence. These equations take the 7 4 form of a nonlinear differential system, on B × S with the characteris- tic degeneracy at the boundary of an edge system, associated with the fibration with fiber S . 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. 1. Introduction Supergravity is a theory of local supersymmetry, which arises in the repre- sentations of super Lie algebras [29]. A supergravity system is a low-energy approximation to string theories [27] and can be viewed as a generalization of Einstein’s equation. Nahm [26] showed that the dimension of the system is at most 11 in http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Annales Henri Poincaré Springer Journals

The Eleven-Dimensional Supergravity Equations on Edge Manifolds

Annales Henri Poincaré , Volume OnlineFirst – May 30, 2018
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Publisher
Springer International Publishing
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
D.O.I.
10.1007/s00023-018-0689-z
Publisher site
See Article on Publisher Site

Abstract

Ann. Henri Poincar´ e Online First c 2018 Springer International Publishing AG, part of Springer Nature Annales Henri Poincar´ e https://doi.org/10.1007/s00023-018-0689-z The Eleven-Dimensional Supergravity Equations on Edge Manifolds Xuwen Zhu Abstract. We study the 11-dimensional supergravity equations which de- scribe a low-energy approximation to string theories and are related to M-theory under the AdS/CFT correspondence. These equations take the 7 4 form of a nonlinear differential system, on B × S with the characteris- tic degeneracy at the boundary of an edge system, associated with the fibration with fiber S . 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. 1. Introduction Supergravity is a theory of local supersymmetry, which arises in the repre- sentations of super Lie algebras [29]. A supergravity system is a low-energy approximation to string theories [27] and can be viewed as a generalization of Einstein’s equation. Nahm [26] showed that the dimension of the system is at most 11 in

Journal

Annales Henri PoincaréSpringer Journals

Published: May 30, 2018

References

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