AdS Vacua, Attractor Mechanism and Generalized Geometries

We consider flux vacua attractor equations in type IIA string theory compactified on generalized geometries with orientifold projections. The four-dimensional N = 1 superpotential in this compactification can be written as the sum of the Ramond-Ramond superpotential and a term described by (non)geometric flux charges. We exhibit a simple model in which supersymmetric AdS and Minkowski solutions are classified by means of discriminants of the two superpotentials. We further study various configurations without Ramond-Ramond flux charges. In this case we find supersymmetric AdS vacua both in the case of compactifications on generalized geometries with SU(3) × SU(3) structures and on manifolds with an SU(3)-structure without nongeometric flux charges. In the latter case, we have to introduce correction terms into the prepotential in order to realize consistent vacua.