Effective actions and N=1 vacuum conditions from SU(3) x SU(3) compactifications

We consider compactifications of typeII string theory on general SU(3) x SU(3) structure backgrounds allowing for a very large set of fluxes, possibly nongeometric ones. We study the effective 4d low energy theory which is a gauged N = 2 supergravity, and discuss how its data are obtained from the formalism of the generalized geometry on T circle plus T*. In particular were late Hitchin's special Kahler metrics on the spaces of even and odd pure spinors to the metric on the supergravity moduli space of internal metric and B-field fluctuations. We derive the N = 1 vacuum conditions from this N = 2 effective action, as well as from its N = 1 truncation. We prove a direct correspondence between these conditions and an integrated version of the pure spinor equations characterizing the N = 1 backgrounds at the ten dimensional level.