Generations of Quarks and Leptons from Noncompact Horizontal Symmetry

The three chiral generations of quarks and leptons may be generated through a spontaneous breakdown of the noncompact horizontal gauge symmetry $G_{H}$ which governs, together with the standard gauge symmetry ${SU(3) \times SU(2) \times U(1)}$, the world in a vectorlike manner. In a framework of supersymmetric theory, the simplest choice ${G_{H}=SU(1,1)}$ works quite well for this scenario in which quarks, leptons and Higgses belong to infinite dimensional unitary representation of $SU(1,1)$. The relevance of the scenario to the hierarchical structure of their Yukawa coupling matrices are discussed.