Non-Abelian Horizontal Symmetry and Anomalous U(1) Symmetry for the Supersymmetric Flavor Problem

Abstract: It is shown that using non-abelian horizontal gauge symmetry and anomalous U(1)_A symmetry in grand unified theories (GUTs), realistic quark and lepton mass matrices including large neutrino mixings can be obtained, while the differences among the scalar fermion masses are sufficiently small for suppression of various flavor changing neutral current (FCNC) processes, especially in E_6 GUT. Combining the Higgs sector, in which doublet-triplet splitting is realized, a complete E_6\times SU(3)_H GUT, in which three generations are unified into a single multiplet, Psi(27,3), is obtained.