Poincare Polynomials and Level Rank Dualities in the $N=2$ Coset Construction

TL;DR

This paper reviews the coset construction of N=2 superconformal models, focusing on Hilbert space construction, Poincaré polynomials, and level-rank dualities, with applications to heterotic string spectra and model equivalences.

Contribution

It introduces an extended Poincaré polynomial for heterotic string spectra and explores level-rank dualities in N=2 coset models, providing new insights into model equivalences.

Findings

Reformulation of Gepner construction using simple currents

Introduction of extended Poincaré polynomial for spectra calculation

Identification of level-rank dualities between models

Abstract

We review the coset construction of conformal field theories; the emphasis is on the construction of the Hilbert spaces for these models, especially if fixed points occur. This is applied to the $N=2$ superconformal cosets constructed by Kazama and Suzuki. To calculate heterotic string spectra we reformulate the Gepner con- struction in terms of simple currents and introduce the so-called extended Poincar\'e polynomial. We finally comment on the various equivalences arising between models of this class, which can be expressed as level rank dualities. (Invited talk given at the III. International Conference on Mathematical Physics, String Theory and Quantum Gravity, Alushta, Ukraine, June 1993. To appear in Theor. Math. Phys.)