Gepner-like description of a string theory on a noncompact singular Calabi–Yau manifold

We investigate a Gepner-like superstring model described by a combination of multiple minimal models and an N=2 Liouville theory. This model is thought to be equivalent to the superstring theory on a singular noncompact Calabi–Yau manifold. We construct the modular invariant partition function of this model, and confirm the validity of an appropriate GSO projection. We also calculate the elliptic genus and Witten index of the model. We find that the elliptic genus is factorised into a rather trivial factor and a non-trivial one, and the non-trivial one has the information on the positively curved base manifold of the cone.