All homogeneous N = 2 M-theory truncations with supersymmetric AdS4 vacua

A bstract We study consistent truncations of M-theory to gauged N = 2 supergravity in four dimensions, based on a large class of SU(3)-structures in seven dimensions. We show that the gauging involves isometries of the vector multiplet scalar manifold as well as the Heisenberg algebra and a special isometry of the hyperscalar manifold. As a result, non-abelian gauge groups and new non-trivial scalar potentials are generated. Then we specialize to all homogeneous SU(3)-structures supporting supersymmetric AdS 4 vacua. These are the Stiefel manifold V 5,2 , the Aloff-Wallach spaces N ( k, l ), the seven-sphere (seen as SU(4)/SU(3) or Sp(2)/Sp(1)) and the M 110 and Q 111 coset spaces. For each of these cases, we describe in detail the N = 2 model and discuss its peculiarities.