PHASES OF N = 2 THEORIES IN 2 DIMENSIONS

By looking at phase transitions which occur as parameters are varied i n supersymmetric gauge theories, a natural relation is found between s igma models based on Calabi-Yau hypersurfaces in weighted projective s paces and Landau-Ginzburg models. The construction permits one to reco ver the known correspondence between these types of models and to grea tly extend it to include new classes of manifolds and also to include models with (0, 2) world-sheet supersymmetry. The construction also pr edicts the possibility of certain physical processes involving a chang e in the topology of space-time.