Eleven-dimensional symmetric supergravity backgrounds, their geometric superalgebras, and a common reduction

Abstract

We present two different families of eleven-dimensional manifolds that admit non-restricted extensions of the isometry algebras to geometric superalgebras. Both families admit points for which the superalgebra extends to a super Lie algebra; on the one hand, a family of N = 1, ν = 3 /4 supergravity backgrounds and, on the other hand, a family of N = 1, ν = 1 supergravity background. Furthermore, both families admit a point that can be identified with an N = 4, ν = 1 /2 six-dimensional supergravity background.