NON-HERMITIAN SYMMETRICAL N = 2 COSET MODELS, POINCARE POLYNOMIALS, AND STRING COMPACTIFICATION

The field identification problem, including fixed point resolution, is solved for the non-hermitian symmetric N = 2 superconformal coset the ories. Thereby these models are finally identified as well-defined mod ular invariant conformal field theories. As an application, the theori es are used as subtheories in N = 2 tensor products with c = 9, which in turn are taken as the inner sector of heterotic superstring compact ifications. All string theories of this type are classified, and the c hiral ring as well as the number of massless generations and anti-gene rations are computed with the help of the extended Poincare polynomial . Several equivalences between a priori different non-hermitian coset theories show up; in particular there is a level-rank duality for an i nfinite series of coset theories based on C-type Lie algebras. Further , some general results for generic N = 2 coset theories 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 m odel is invariant under charge conjugation.