Classical and Quantum Calabi-Yau Manifolds
It has been clear for some time now that not all compactification schemes used to construct consistent Heterotic String vacua are independent. This is particularly obvious in the case of Calabi-Yau manifold compactifications and the c = 9, N — 2 minimal superconformai tensor models. In two case studies  Gepner presented compelling evidence for the existence of a deep relation between exact models and Calabi-Yau manifolds (CYs). Gepner showed that not only do these two models have the same massless spectrum and exhibit the same discrete symmetries, but that the fields also transform in the same way under discrete symmetry transformations. Although somewhat indirect, this evidence lead Gepner to conjecture that all exact N = 2 superconformai models correspond to Calabi-Yau manifolds.
KeywordsYukawa Coupling Chern Class Discrete Symmetry Current Algebra Euler Number
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