Type-IIA flux compactifications and N=4 gauged supergravities

We establish the precise correspondence between Type-IIA flux compactifications preserving an exact or spontaneously broken = 4 supersymmetry in four dimensions, and gaugings of their effective = 4 supergravities. We exhibit the explicit map between fluxes and Bianchi identities in the higher-dimensional theory and generalized structure constants and Jacobi identities in the reduced theory, also detailing the origin of gauge groups embedded at angles in the duality group. We present AdS 4 solutions of the massive Type-IIA theory with spontaneous breaking to = 1, at small string coupling and large volume, and discuss their dual CFT 3. © 2009 SISSA.