Heterotic String/F-theory Duality from Mirror Symmetry
arXiv:hep-th/9811217
Abstract
We use local mirror symmetry in type IIA string compactifications on Calabi-Yau n+1 folds to construct vector bundles on (possibly singular) elliptically fibered Calabi-Yau n-folds Z_n. The interpretation of these data as valid classical solutions of the heterotic string compactified on Z_n proves F-theory/heterotic duality at the classical level. Toric geometry is used to establish a systematic dictionary that assigns to each given toric n+1-fold a toric n fold Z_n 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)\times SU(2) gauge groups. As another application we find non-perturbative gauge enhancements of the heterotic string on singular Calabi-Yau manifolds and new non-perturbative dualities relating heterotic compactifications on different manifolds.
63 pages, harvmac, 2 figures, v2: references added, extended explanations on non-perturbative five-branes and the identification of a line bundle that is an important characteristic of the gauge background