CPviolation and Yukawa couplings in superstring models: A four-generation example

We present a detailed discussion of the pattern of Yukawa couplings and CP violation in a superstring ${\mathrm{E}}_6$ model built on a ${\mathrm{CP}}^4$-based Calabi-Yau manifold, with $Z_5$×$Z_5^{\mathcal{’}}$ discrete symmetry. Embedding the two $Z_5$’s into the ${\mathrm{E}}_6$ group leads to a drastically different pattern of Yukawa couplings. The model is presented more as an illustration of the steps involved in the calculation of Yukawa couplings in a generic Calabi-Yau manifold rather than as a realistic model of quarks and leptons.