A family of non-restricted D=11 geometric supersymmetries

Abstract

We construct a two parameter family of irreducible, eleven-dimensional, indecomposable, non-flat Cahen-Wallach spaces with non-restricted geometric supersymmetry of fraction ν = 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 ν = 1/2 in dimension six and a non-restricted N = 2 geometric supersymmetry with ν = 3/4 in dimension nine.