Singular Calabi-Yau Manifolds and ADE Classification of CFTs

Details Singular Calabi-Yau Manifolds and ADE Classification of CFTs Singular Calabi-Yau Manifolds and ADE Classification of CFTs

2000-09-30

arxiv.org/abs/hep-th/0010002v1

Nucl.Phys. B599 (2001) 334-360

Physics

High Energy Physics

High Energy Physics - Theory

31 pages, no figure

Scientific paper

10.1016/S0550-3213(00)00760-4

We study superstring propagations on the Calabi-Yau manifold which develops an isolated ADE singularity. This theory has been conjectured to have a holographic dual description in terms of N=2 Landau-Ginzburg theory and Liouville theory. If the Landau-Ginzburg description precisely reflects the information of ADE singularity, the Landau-Ginzburg model of $D_4,E_6,E_8$ and Gepner model of $A_2\otimes A_2, A_2\otimes A_3, A_2\otimes A_4$ should give the same result. We compute the elements of $D_4,E_6,E_8$ modular invariants for the singular Calabi-Yau compactification in terms of the spectral flow invariant orbits of the tensor product theories with the theta function which encodes the momentum mode of the Liouville theory. Furthermore we find the interesting identity among characters in minimal models at different levels. We give the complete proof for the identity.

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