Fluxes and gaugings: N = 1 effective superpotential

We illustrate the correspondence between the N = 1 superstring compactifications with fluxes, the N = 4 gauged supergravities and the superpotential and Kähler potential of the effective N = 1 supergravity in four dimensions. In particular we derive, in the presence of general fluxes, the effective N = 1 supergravity theory associated to the type IIA orientifolds with D6 branes, compactified on T⁶/(Z₂ × Z ₂). We construct explicit examples with different features: in particular, new IIA no-scale models, new models with cosmological interest and a model which admits a supersymmetric AdS₄ vacuum with all seven main moduli (S, T_A, U_A, A = 1,2,3) stabilized.