ADE quantum Calabi-Yau manifolds

Abstract

We identify a class of weighted complete intersection Calabi-Yau manifolds with Gepner models involving the non-diagonal invariants. To this end we extend previous calculations of the spectrum to all tensor models with all possible affine invariants - the ADE-invariants. Generalizing recent results on the relation between Gepner models with diagonal invariants and Calabi-Yau manifolds we describe how to relate these new models to manifolds via Landau-Ginzburg potentials. We also describe how to compute the spectrum for these Calabi-Yau manifolds using the theory of resolutions of singularities. The Landau-Ginzburg type computation of the spectra leads to complete agreement with both, the exact calculation and the manifold results.