A family of non-restricted $D=11$ geometric supersymmetries

TL;DR

This paper constructs a family of eleven-dimensional geometric supersymmetries with specific properties, exploring their moduli space and connections to lower-dimensional supersymmetries, revealing new non-restricted supersymmetric spaces.

Contribution

It introduces a two-parameter family of indecomposable Cahen-Wallach spaces with unique non-restricted geometric supersymmetry in eleven dimensions, expanding the classification of supersymmetric backgrounds.

Findings

Constructed a two-parameter family of eleven-dimensional supersymmetric spaces.

Identified the moduli space as a compact interval with two special points.

Connected these spaces to lower-dimensional restricted and non-restricted supersymmetries.

Abstract

We construct a two parameter family of eleven-dimensional indecomposable Cahen-Wallach spaces with irreducible, non-flat, non-restricted geometric supersymmetry of fraction $\nu=\tfrac{3}{4}$. Its compactified moduli space can be parametrized by a compact interval with two points corresponding to two non-isometric, decomposable spaces. These singular spaces are associated to a restricted $N=4$ geometric supersymmetry with $\nu=\tfrac{1}{2}$ in dimension six and a non-restricted $N=2$ geometric supersymmetry with $\nu=\tfrac{3}{4}$ in dimension nine.