Gauge Hierarchy in ${\bf SU(3)_c \times SU(3)_L \times SU(3)_R}$ and Low Energy Implication

Abstract

We explore the gauge hierarchy problem within the framework of supersymmetric $SU(3)_c \times SU(3)_L \times SU(3)_R$ with a minimal set of higgs supermultiplets. Imposition of a suitable discrete (alternatively $R$) symmetry `prevents' the electroweak higgs doublets from becoming superheavy through renormalizable couplings. A full resolution of the problem requires consideration of the non-renormalizable couplings which play an essential role. Other key differences from the minimal supersymmetric $SU(5)$ model include the fact that the proton is stable and that an effective $5 + \bar{5}$ supermultiplet appears around the $TeV$ mass scale.