Realization of AdS Vacua in Attractor Mechanism on Generalized Geometries

We evaluate 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 is described as a sum of the Ramond-Ramond superpotential and the one described by the (non)geometric flux charges. We demonstrate a single modulus model in which supersymmetric AdS and Minkowski solutions are classified by means of the discriminants of the two superpotentials. We further study various configurations without the Ramond-Ramond flux charges. There we also find supersymmetric AdS vacua both in the case of compactifications on the generalized geometry with SU(3) × SU(3) structures, and on the manifold with SU(3)-structure without the nongeometric flux charges. Especially, in the latter case, we have to introduce a correction into the prepotential of the special geometry in order to realize consistent vacua. This deformation is interpreted as the α corrections caused by the back reaction of the geometric fluxes on the compactified space.