Half-BPS quotients in M-theory: ADE with a twist

TL;DR

This paper classifies certain supersymmetric M-theory backgrounds involving quotients of the 7-sphere, revealing new solutions linked to specific ADE subgroups and automorphisms, expanding the understanding of half-BPS configurations.

Contribution

It provides a comprehensive classification of half-BPS AdS_4 x X^7 backgrounds in M-theory involving ADE quotients with automorphisms, including novel solutions.

Findings

New half-BPS quotients associated with D_n (n>5), E_7, and E_8 subgroups.

Classification in terms of ADE subgroups and automorphisms.

Identification of novel solutions with specific automorphisms.

Abstract

We classify Freund-Rubin backgrounds of eleven-dimensional supergravity of the form AdS_4 x X^7 which are at least half BPS; equivalently, smooth quotients of the round 7-sphere by finite subgroups of SO(8) which admit an (N>3)-dimensional subspace of Killing spinors. The classification is given in terms of pairs consisting of an ADE subgroup of SU(2) and an automorphism defining its embedding in SO(8). In particular we find novel half-BPS quotients associated with the subgroups of type D_n (for n>5), E_7 and E_8 and their outer automorphisms.