Reducing democratic type II supergravity on SU(3)×SU(3) structures

Type II supergravity on backgrounds admitting SU(3)×SU(3) structure and general fluxes is considered. Using the generalized geometry formalism, we study dimensional reductions leading toN = 2 gauged supergravity in four dimensions, possibly with tensor multiplets. In particular, a geometric formula for the full N = 2 scalar potential is given. Then we implement a truncation ansatz, and derive the complete N = 2 bosonic action. While the NSNS contribution is obtained via a direct dimensional reduction, the contribution of the RR sector is computed starting from the democratic formulation and demanding consistency with the reduced equations of motion. ∗ unité mixte du CNRS et de l’École Normale Supérieure associée à l’UPMC Univ. Paris 06