We derive the effective N=1, D=4 supergravity for the seven main moduli of type IIA orientifolds with D6 branes, compactified on T^6/(Z_2xZ_2) in the presence of general fluxes. We illustrate and apply a general method that relates the N=1 effective Kahler potential and superpotential to a consistent truncation of gauged N=4 supergravity. We identify the correspondence between various admissible fluxes, N=4 gaugings and N=1 superpotential terms. We construct explicit examples with different features: in particular, new IIA no-scale models and a model which admits a supersymmetric AdS_4 vacuum with all seven main moduli stabilized

We compute and analyse a variety of four-derivative gravitational terms in the effective action of six-and four-dimensional type II string ground states with N = 4 supersymmetry. In six dimensions, we compute the relevant perturbative corrections for the type II string compactified on K3. In four dimensions we do analogous computations for several models with (4, 0) and (2, 2) supersymmetry. Such ground states are related by heterotic-type II duality or type II-type II U-duality. Perturbative computations in one member of a dual pair give a non-perturbative result in the other member. In particular, the exact CP-even R 2 coupling on the (2, 2) side reproduces the tree-level term plus NS 5-brane instanton contributions on the (4, 0) side. On the other hand, the exact CP-odd coupling yields the one-loop axionic interaction aR ∧ R together with a similar instanton sum. In a subset of models, the expected breaking of the SL(2, Z) S S-duality symmetry to a Γ(2) S subgroup is observed on the non-perturbative thresholds. Moreover, we present a duality chain that provides evidence for the existence of heterotic N = 4 models in which N = 8 supersymmetry appears at strong coupling.