On the geometric interpretation of \(N=2\) superconformal theories. (English) Zbl 1052.32502
Summary: We clarify certain important issues relevant for the geometric interpretation of a large class of \(N=2\) superconformal theories. By fully exploiting the phase structure of these theories (discovered in earlier works) we are able to clearly identify their geometric content. One application is to present a simple and natural resolution to the question of what constitutes the mirror of a rigid Calabi-Yau manifold. We also discuss some other models with unusual phase diagrams that highlight some subtle features regarding the geometric content of conformal theories.
MSC:
| 32G81 | Applications of deformations of analytic structures to the sciences |
| 14J32 | Calabi-Yau manifolds (algebro-geometric aspects) |
| 32G20 | Period matrices, variation of Hodge structure; degenerations |
| 32J81 | Applications of compact analytic spaces to the sciences |
| 81T40 | Two-dimensional field theories, conformal field theories, etc. in quantum mechanics |
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