Abstract
We use local mirror symmetry in type IIA string compactifications on Calabi–Yau n + 1 folds Xn+1 to construct vector bundles on (possibly singular) elliptically fibered Calabi–Yau n-folds Zn. The interpretation of these data as valid classical solutions of the heterotic string compactified on Zn proves Ftheory/heterotic duality at the classical level. Toric geometry is used to establish a systematic dictionary that assigns to each given toric n+1-fold Xn+1 a toric n fold Zn together with a specific family of sheafs on it. This allows for a systematic construction of phenomenologically interesting d = 4 N = 1 heterotic vacua, e.g. on deformations of the tangent bundle, with grand unified and SU(3)× SU(2) gauge groups. As another application we find nonperturbative gauge enhancements of the heterotic string on singular Calabi–Yau manifolds and new non-perturbative dualities relating heterotic compactifications on different manifolds. November 1998 1 berglund@itp.ucsb.edu 2 Peter.Mayr@cern.ch
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