On $\mathcal{N} = 1$ 4d effective couplings for F-theory and heterotic vacua

Abstract

We show that certain superpotential and Kähler potential couplings of $\mathcal{N} = 1$ supersymmetric compactifications with branes or bundles can be computed from Hodge theory and mirror symmetry. This applies to F-theory on a Calabi–Yau four-fold and three-fold compactifications of type II and heterotic strings with branes. The heterotic case includes a class of bundles on elliptic manifolds constructed by Friedmann, Morgan and Witten. Mirror symmetry of the four-fold computes non-perturbative corrections to mirror symmetry on the three-folds, including D-instanton corrections. We also propose a physical interpretation for the observation byWarner that relates the deformation spaces of certain matrix factorizations and the periods of non-compact four-folds that are ALE fibrations.