All symmetric space solutions of eleven-dimensional supergravity

TL;DR

This paper classifies all symmetric space solutions in eleven-dimensional supergravity, identifying which are supersymmetric and analyzing their algebraic structures, thereby completing prior work in this area.

Contribution

It provides a complete classification of symmetric space solutions in eleven-dimensional supergravity, including supersymmetry analysis and superisometry algebra derivation.

Findings

99 AdS geometries identified, only some are supersymmetric

Supersymmetric solutions correspond to known M-brane near-horizon limits

Superisometry algebra for symmetric backgrounds derived

Abstract

We find all symmetric space solutions of eleven-dimensional supergravity completing an earlier classification by Figueroa-O'Farrill. They come in two types: AdS solutions and pp-wave solutions. We analyze the supersymmetry conditions and show that out of the 99 AdS geometries the only supersymmetric ones are the well known backgrounds arising as near-horizon limits of (intersecting) M-branes and preserving 32, 16 or 8 supersymmetries. The general form of the superisometry algebra for symmetric space backgrounds is also derived.