Generalized string functions of N = 1 space-time supersymmetric string vacua

We present a dual formulation of the construction of N = 2 nonlinear σ-model type conformal field theories with c = 9 which are mainly used as internal sectors of Calabi-Yau heterotic string compactifications. The supercurrents G±(z) and the higher components of the spectral flow superfields X±(z) + θ±Y±(z) turn out in each case to be tensor products of two simple currents of a c = 1 and a non-supersymmetric parafermionic c = 8 CFT. The characters of the latter model can be regarded as string functions of the coset σU(1). In particular, for the (1)9 Gepner model we discuss these string functions in detail, realizing this model contains a broken E8 gauge symmetry of which only the abelian subalgebra remains a symmetry of the spectrum. As an example, we construct a simple model leading to a string theory with a massless spectrum of 36 E6 generations and an extended gauge symmetry E6 × SU(3)4.