Gepner-like Description of a String Theory on a Noncompact Singular Calabi-Yau Manifold

TL;DR

This paper constructs and analyzes a superstring model combining minimal models and Liouville theory, providing insights into string theory on singular noncompact Calabi-Yau manifolds through modular invariants and elliptic genus calculations.

Contribution

It introduces a Gepner-like superstring model for singular noncompact Calabi-Yau manifolds and confirms its consistency via modular invariance and GSO projection.

Findings

Modular invariant partition function constructed

Elliptic genus factorizes revealing base manifold information

Model confirms superstring theory on singular Calabi-Yau manifolds

Abstract

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 factorises 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.