The eleven dimensional supergravity equations on edge manifolds

TL;DR

This paper analyzes the complex eleven-dimensional supergravity equations on edge manifolds, computing linearized solutions and describing the moduli space near specific states using advanced geometric and analytical techniques.

Contribution

It introduces a novel analysis of supergravity equations on edge manifolds, computing indicial roots and characterizing the moduli space near Freund--Rubin states.

Findings

Computed indicial roots of the linearized system.

Proved the moduli space near Freund--Rubin states is parametrized by three pairs of data.

Applied edge calculus and scattering theory to supergravity equations.

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.