Localized Modes in Type II and Heterotic Singular Calabi-Yau Conformal Field Theories

TL;DR

This paper constructs modular invariant string partition functions for type II and heterotic theories on singular Calabi-Yau spaces, analyzing localized massless modes and proposing a three-generation E6 model at the singularity.

Contribution

It introduces new modular invariant partition functions for string compactifications on singular Calabi-Yau spaces, with detailed analysis of localized massless spectra and a novel three-generation model.

Findings

New modular invariant, space-time supersymmetric partition functions constructed.

Detailed analysis of localized massless modes at singularities.

Proposal of a three-generation E6 model localized at the singularity.

Abstract

We consider type II and heterotic string compactifications on an isolated singularity in the noncompact Gepner model approach. The conifold-type ADE noncompact Calabi-Yau threefolds, as well as the ALE twofolds, are modeled by a tensor product of the SL(2,R)/U(1) Kazama-Suzuki model and an N=2 minimal model. Based on the string partition functions on these internal Calabi-Yaus previously obtained by Eguchi and Sugawara, we construct new modular invariant, space-time supersymmetric partition functions for both type II and heterotic string theories, where the GSO projection is performed before the continuous and discrete state contributions are separated. We investigate in detail the massless spectra of the localized modes. In particular, we propose an interesting three generation model, in which each flavor is in the 27+1 representation of E6 and localized on a four-dimensional space-time residing at the tip of the cigar.