Non-perturbative superpotentials in F-theory and string duality

We use open-closed string duality between F-theory on K3 x K3 and type II strings on CY manifolds without branes to study non-perturbative superpotentials in generalized flux compactifications. On the F-theory side we obtain the full flux potential including D3-instanton contributions and show that it leads to an explicit and simple realization of the three ingredients of the KKLT model for stringy dS vacua. The D3-instanton contribution is highly non-trivial, can be systematically computed including the determinant factors and demonstrates that a particular flux lifts very effectively zero modes on the instanton. On the closed string side, we describe a generalization of the Gukov-Vafa-Witten superpotential for type II strings on generalized CY manifolds, depending on all moduli multiplets.