Noncompact Gepner Models with Discrete Spectra

TL;DR

This paper explores a noncompact Gepner model combining SL(2,R)/U(1) and N=2 minimal models, revealing how discrete series relate to vanishing cohomology and cycles in noncompact Calabi-Yau manifolds, with calculations of elliptic genus and Witten indices.

Contribution

It demonstrates the connection between discrete series in noncompact Gepner models and geometric features like vanishing cohomology and cycles, providing explicit calculations.

Findings

Discrete series contain vanishing cohomology and cycles.

Elliptic genus matches vanishing cohomology in ALE models.

Open string Witten indices align with intersection forms.

Abstract

We investigate a noncompact Gepner model, which is composed of a number of SL(2,R)/U(1) Kazama-Suzuki models and N=2 minimal models. The SL(2,R)/U(1) Kazama-Suzuki model contains the discrete series among the SL(2,R) unitary representations as well as the continuous series. We claim that the discrete series contain the vanishing cohomology and the vanishing cycles of the associated noncompact Calabi-Yau manifold. We calculate the Elliptic genus and the open string Witten indices. In the A_{N-1} ALE models, they actually agree with the vanishing cohomology and the intersection form of the vanishing cycles.