Yukawa couplings and phenomenology of a three-generation superstring model with a new complex structure

We consider the ${\mathrm{CP}}^3$×${\mathrm{CP}}^3$-based Calabi-Yau manifold proposed by Yau to compactify the ten-dimensional superstring models to four dimensions and study the implications for quark-lepton physics by choosing a different set of hypersurfaces in the ${\mathrm{CP}}^3$×${\mathrm{CP}}^3$ space than considered previously. The new set of hypersurfaces are obtained by identifying points related by $Z_3$ symmetry which shifts $x_i$→$x_{i+1\mathrm{}}$ and $y_i$→$y_{i+1\mathrm{}}$ (mod 3) for i=1,...,3. We study the discrete symmetries of this manifold and obtain transformation properties of the various 27 and 27¯ fields under these symmetries. This is followed by an explicit calculation of the Yukawa couplings of (27${)}^3$ type and a discussion of the ${\mathrm{E}}_6$-singlet fields and their couplings. We then discuss some phenomenological implications of the model.