Noncompact Gepner Models with Discrete Spectra

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.