Abstract
In this paper we show that D = 11 supergravity admits an infinite discrete class of solutions having the phenomenological group SU(3) ⊗ SU(2) ⊗ U(1) as a symmetry of the internal space M 7. These solutions lead, in dimensional reduction, to SU(3) ⊗ SU(2) ⊗ U(1) gauge fields. In general all these spaces produce a complete breaking of supersymmetry except in one case where N = 2 supersymmetry survives. The parameter which classifies the solutions is a rational number q/ p which describes the embedding of the stability subgroup SU(2) ⊗ U(1) ⊗ U(1) of M 7 in SU(3) ⊗ SU(2) ⊗ U(1). For all q/ p ≠ 1 the holonomy group is SO(7) and all supersymmetries are broken. For q/ p = 1 the holonomy group is SU(3) and two supersymmetries survive. In this last case we can also find a solution with internal photon curl F αβγδ ≠ 0 . It breaks all sypersymmetries.
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