Non-Hermitian Symmetric N=2 Coset Models, Poincare Polynomials, and String Compactification

TL;DR

This paper resolves the field identification problem for non-hermitian symmetric N=2 superconformal coset theories, classifies related string compactifications, and explores dualities and invariances using Poincare polynomials.

Contribution

It provides the first complete solution to fixed point resolution in these coset models and applies the results to classify heterotic string compactifications with detailed spectral data.

Findings

Resolved the field identification problem for non-hermitian symmetric N=2 cosets.

Classified string theories based on these models and computed massless spectra.

Discovered level-rank dualities and invariances in Ramond ground states.

Abstract

The field identification problem, including fixed point resolution, is solved for the non-hermitian symmetric $N=2$ superconformal coset theories. Thereby these models are finally identified as well-defined modular invariant CFTs. As an application, the theories are used as subtheories in tensor products with $c=9$, which in turn are taken as the inner sector of heterotic superstring compactifications. All string theories of this type are classified, and the chiral ring as well as the number of massless generations and anti-generations are computed with the help of the extended Poincare polynomial. Several equivalences between a priori different non-hermitian cosets show up; in particular there is a level-rank duality for an infinite series based on $C$ type Lie algebras. Further, some general results for generic $N=2$ cosets are proven: a simple formula for the number of identification currents is found, and it is shown that the set of Ramond ground states of any $N=2$ coset model is invariant under charge conjugation.