Generalization of Calabi-Yau/Landau-Ginzburg correspondence

Details Generalization of Calabi-Yau/Landau-Ginzburg correspondence Generalization of Calabi-Yau/Landau-Ginzburg correspondence

1999-11-27

arxiv.org/abs/hep-th/9911220v1

JHEP 0002 (2000) 028

Physics

High Energy Physics

High Energy Physics - Theory

19 pages, Latex

Scientific paper

10.1088/1126-6708/2000/02/028

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 k2. 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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