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 N = 4 supersymmetry in four dimensions, and gaugings of their effective N = 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 AdS4 solutions of the massive Type-IIA theory with spontaneous breaking to N = 1, at small string coupling and large volume, and discuss their dual CFT3.