A supersymmetric grand unified model with noncompact horizontal symmetry

In a supersymmetric SU(5) grand unified model with a horizontal symmetry SU(1, 1), we discuss spontaneous generation of generations to produce three chiral generations of quarks and leptons and one generation of Higgses by using one structure field with a half-integer spin of SU(1, 1) and two structure fields with integer spins. In particular, the colored Higgses can disappear without fine-tuning. The difference of the Yukawa coupling matrices between the down-type quarks and charged leptons is discussed. We show that some special SU(1, 1) weight assignments include R-parity as a discrete subgroup, and R-parity remains even after we take into account the SU(1, 1) breaking effects from all the vacuum expectation values of the structure and matter fields. The assignments forbid the baryon and/or lepton number violating terms except a superpotential quartic term including a coupling of two lepton doublets and two up-type Higgses. We discuss how to generate sizable neutrino masses. We show that the proton decay derived from the colored Higgses is highly suppressed.