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

TL;DR

This paper explores two families of eleven-dimensional supergravity backgrounds with extended symmetry structures, revealing points where these backgrounds relate to lower-dimensional supergravity configurations.

Contribution

It introduces new families of eleven-dimensional manifolds with extended geometric superalgebras and identifies special points linking to six-dimensional supergravity backgrounds.

Findings

Existence of two families of eleven-dimensional manifolds with extended superalgebras.

Identification of points where superalgebras extend to super Lie algebras.

Connection to six-dimensional supergravity backgrounds at specific points.

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 $N=1$, $\nu={}^3\!/\!_4$ supergravity backgrounds and, on the other hand, a family of $N=1$, $\nu=1$ supergravity background. Furthermore, both families admit a point that can be identified with an $N=4$, $\nu={}^1\!/\!_2$ six-dimensional supergravity background.