Poincaré polynomials and level rank dualities in the N=2 coset construction

We review the coset construction of conformal field theories; the emphasis is on the Hilbert spaces for these models, especially if fixed points occur. This is applied to theN=2 superconformal cosets constructed by Kazama and Suzuki. To calculate heterotic string spectra we reformulate the Gepner construction in terms of simple currents and introduce the so-called extended Poincaré polynomial. We finally comment on the various equivalences arising between models of this class, which can be expressed as level rank dualities.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 98. No. 3, pp. 467–478, March, 1994.