Non-perturbative N=1 strings from geometric singularities

The study of curved D-brane geometries in type II strings implies a general relation between local singularities W of Calabi-Yau manifolds and gravity -free supersymmetric quantum field theories. The minimal supersymmetric cas e is described by F-theory compactifications on W and can be used as a star ting point to define minimal supersymmetric heterotic string compactificati ons on compact Calabi-Yau manifolds with holomorphic, stable gauge backgrou nds. The geometric construction generalizes to non-perturbative vacua with 5-branes and provides a framework to study non-perturbative dynamics of the heterotic theory.