Abstract
We classify Freund-Rubin backgrounds of eleven-dimensional supergravity of the form AdS4 × X7 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 Dn ≥ 6, E7 and E8 and their outer automorphisms.
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