Phenomenological clues for discrete symmetries in superstring theories

It is shown that within the framework of the ${\mathrm{E}}_8$×${\mathrm{E}}_8$ heterotic superstring if the Yukawa superpotential of the effective four-dimensional ${\mathrm{E}}_6$ gauge theory is required to lead in a natural way to (i) no rapid proton decay, (ii) Fritzsch-type quark and charged-lepton mass matrices, and (iii) naturally small neutrino masses generated through radiative corrections, then for three generations a minimal $Z_2$×$Z_5$ symmetry is required. A minimal model based on this discrete symmetry is suggested and discussed. The generalization for more than three generations is analyzed.