Generations of Quarks and Leptons from Noncompact Horizontal Symmetry

Abstract

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.

Comments: 22 pages, e-mail: inoue@yukawa.kyoto-u.ac.jp , Plain Tex, YITP/K-1089