Special Kahler geometry and Landau-Ginzburg theories

Special Kahler geometry is a geometric structure behind coupling constants of d=4 N=2 supersymmetric gauge theories. It appears naturally in superstring compactifications on Calabi-Yau threefolds. Coupling constants are computed from complex and Kahler moduli geometry of the Calabi-Yau manifold and their explicit computation is not simple. In this talk I will explain a recently developed method to compute special geometry based on the correspondence of Calabi-Yau non-linear sigma models and supersymmetric Landau-Ginzburg orbifolds. This method allowed to compute special geometry for a huge class of manifolds for which no explicit computations were done before.