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We show that certain superpotential and Kahler potential couplings of N=1supersymmetric compactifications with branes or bundles can be computed fromHodge theory and mirror symmetry. This applies to F-theory on a Calabi-Yaufour-fold and three-fold compactifications of type II and heterotic stringswith branes. The heterotic case includes a class of bundles on ellipticmanifolds constructed by Friedmann, Morgan and Witten. Mirror symmetry of thefour-fold computes non-perturbative corrections to mirror symmetry on thethree-folds, including D-instanton corrections. We also propose a physicalinterpretation for the observation by Warner that relates the deformationspaces of certain matrix factorizations and the periods of non-compact 4-foldsthat are ALE fibrations.

On N=1 4d Effective Couplings for F-theory and Heterotic Vacua