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Fluxes and gaugings: N = 1 effective superpotentials

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 $T^6/(Z_2 \times Z_2)$. 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 AdS$_4$ vacuum with all seven main moduli ($S, T_A, U_A,A=1,2,3$) stabilized.