M-theory on seven-dimensional manifolds with SU(3) structure

In this paper we study M-theory compactifications on seven-dimensional manifolds with SU(3) structure. As such manifolds naturally pick out a specific direction, under certain assumptions regarding the expansion basis the resulting effective theory can be cast into a form which is similar to type IIA compactifications to four dimensions. We derive the gravitino mass matrix in four dimensions and show that for different internal manifolds (torsion classes) the vacuum preserves either no supersymmetry, or N = 2 supersymmetry or, through spontaneous partial supersymmetry breaking, N = 1 supersymmetry. For the latter case we derive the effective N = 1 theory and give explicit examples where all the moduli are stabilised without the need of non-perturbative effects.