A Supersymmetric Grand Unified Model with Noncompact Horizontal Symmetry

TL;DR

This paper proposes a supersymmetric SU(5) grand unified model with a noncompact SU(1,1) horizontal symmetry, explaining generation structure, R-parity conservation, and suppressed proton decay through specific symmetry breaking and field assignments.

Contribution

It introduces a novel SU(1,1) horizontal symmetry framework that naturally generates three generations, maintains R-parity, and suppresses proton decay without fine-tuning.

Findings

Colored higgses can disappear without fine-tuning

R-parity remains after symmetry breaking

Proton decay is highly suppressed

Abstract

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 VEVs 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.