Coset Character Identities in Superstring Compactifications

TL;DR

This paper uses coset character identities to analyze superstring compactifications, demonstrating supersymmetry-related vanishing of partition functions and providing evidence for dualities involving superconformal field theories.

Contribution

It applies coset character identities to both compact and noncompact Gepner models, revealing supersymmetry properties and supporting holographic duality conjectures.

Findings

Partition functions vanish due to spacetime supersymmetry.

Discrete parts of models show expected vanishing factors.

Continuous parts suggest doubled supersymmetry, supporting superconformal duality.

Abstract

We apply the coset character identities (generalization of Jacobi's abstruse identity) to compact and noncompact Gepner models. In the both cases, we prove that the partition function actually vanishes due to the spacetime supersymmetry. In the case of the compact models and discrete parts of the noncompact models, the partition function includes the expected vanishing factor. But the character identities used to the continuous part of the noncompact models suggest that these models have twice as many supersymmetry as expected. This fact is an evidence for the conjecture that the holographically dual of the string theory on an actually singular Calabi-Yau manifold is a super CONFORMAL field theory. The extra SUSY charges are interpreted as the superconformal S generators.