Symmetric M-Theory Backgrounds

TL;DR

This paper classifies all symmetric solutions of eleven-dimensional supergravity by analyzing the geometric structures and invariant 4-forms, providing a comprehensive catalog of such backgrounds.

Contribution

It offers a complete classification of symmetric supergravity backgrounds, including explicit descriptions of the geometric spaces and invariant 4-forms involved.

Findings

Classified all symmetric supergravity backgrounds in eleven dimensions.

Identified possible geometric structures: Cahen-Wallach spaces and products of AdS with Riemannian symmetric spaces.

Determined F-moduli spaces for most cases.

Abstract

We classify symmetric backgrounds of eleven-dimensional supergravity up to local isometry. In other words, we classify triples (M,g,F), where (M,g) is an eleven-dimensional lorentzian locally symmetric space and F is an invariant 4-form, satisfying the equations of motion of eleven-dimensional supergravity. The possible (M,g) are given either by (not necessarily nondegenerate) Cahen-Wallach spaces or by products AdS_d x M for 1 < d < 8 and M a not necessarily irreducible riemannian symmetric space of dimension 11-d. In most cases we determine the corresponding F-moduli spaces.