Flux vacua in type II supergravity theories
We first give a review of the geometrical techniques (in particular G-structures and Generalized Complex Geometry) that are currently used in the study of supersymmetric N=1 compactifications. Then we focus on the study of type IIB compactifications to four dimensional Anti de Sitter vacua with N=1 supersymmetry. We give the general conditions that supersymmetry imposes on the solutions in particular, the internal manifold must have SU(2)-structure. Then we perform an exhaustive search of such vacua on cosets and group manifold. With some assumptions on the SU(2) torsion classes and constant dilaton and warp factor, we find that such vacua are very rare : two on cosets and five on group manifolds. All of them are required to include intersecting O5 and O7-planes. This also means that there exist no sourceless AdS4 vacua. We then study scales separation on the vacua in order to look give some insights for four dimensional effective theory and found that only two of them admit scales separation.