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Phases of \(N=2\) theories in two dimensions. (English) Zbl 0910.14020

Summary: By looking at phase transitions which occur as parameters are varied in supersymmetric gauge theories, a natural relation is found between sigma models based on Calabi-Yau hypersurfaces in weighted projective spaces and Landau-Ginzburg models. The construction permits one to recover the known correspondence between these types of models and to greatly extend it to include new classes of manifolds and also to include models with \((0,2)\) world-sheet supersymmetry. The construction also predicts the possibility of certain physical processes involving a change in the topology of space-time.
Reprinted in Mirror Symmetry II, AMS/IP Stud. Adv. Math. 1, 143-211 (1997; see the following review).

MSC:

14J32 Calabi-Yau manifolds (algebro-geometric aspects)
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
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