Generation structure and superpotential in string compactification on N = 2 superconformal field theory

We study the spectrum of heterotic string theory with four generations compactified on the fifth tensor product of the N = 2 superconformal field theory with level three (35 theory). Following the observation that this compactification is equivalent to Y(4;5)/Z5 x Z5 Calabi-Yau compactification, we concretely represent quarks and leptons by the spectrum of 35 theory. This makes it possible to write down exactly the superpotential, in particular, Yukawa couplings for physical quarks and leptons