The eleven dimensional supergravity equations on edge manifolds

Abstract

We study the eleven 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 non-linear differential system, on ${\mathbb{B}}^7\times {\mathbb{S}}^4$ with the characteristic degeneracy at the boundary of an edge system, associated to 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, 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.

48 pages, 1 figure. To appear in Annales Henri Poincare

References in corpus (2)

• On Flux Quantization In M-Theory And The Effective Action
• Penrose limits, supergravity and brane dynamics