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arXiv · hep-th/9911220

Generalization of Calabi-Yau/Landau-Ginzburg correspondence

Tohru Eguchi·Masao Jinzenji
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Abstract

We discuss a possible generalization of the Calabi-Yau/Landau-Ginzburg correspondence to a more general class of manifolds. Specifically we consider the Fermat type hypersurfaces $M_N^k$: $\sum_{i=1}^N X_i^k =0$ in ${\bf CP}^{N-1}$ for various values of k and N. When k 2. We assume that this massless sector is described by a Landau-Ginzburg (LG) theory of central charge $c=3N(1-2/k)$ with N chiral fields with U(1) charge $1/k$. We compute the topological invariants (elliptic genera) using LG theory and massive vacua and compare them with the geometrical data. We find that the results agree if and only if k=even and N=even. These are the cases when the hypersurfaces have a spin structure. Thus we find an evidence for the geometry/LG correspondence in the case of spin manifolds.

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Tohru Eguchi, Masao Jinzenji. 1999-11-27. Generalization of Calabi-Yau/Landau-Ginzburg correspondence. https://doi.org/10.1088/1126-6708%2F2000%2F02%2F028

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