Noncompact Gepner models with discrete spectra

We investigate a noncompact Gepner model, which is composed of a number of SL(2, R)/U(1) Kanama-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) uni tary representations as well as the continuous series. We claim that the di screte series contain the vanishing cohomology and the vanishing cycles of the associated noncompact Calabi-Yau manifold. We calculate the Elliptic ge nus and the open string Witten indices. In the A(N-1) ALE models, they actu ally agree with the vanishing cohomology and the intersection form of the v anishing cycles. (C) 2001 Elsevier Science B.V. All rights reserved.