Gauge Hierarchy, Planck Scale Corrections And The Origin of GUT Scale In Supersymmetric $(SU(3))^3$

Abstract

Within a supersymmetric unified framework we explore the resolution of the gauge hierarchy problem taking account of the non-renormalizable terms in the superpotential. For $[SU(3)]^3$ supplemented by a discrete R parity, we find the remarkable property that the vacuum configuration corresponding to the correct gauge symmetry breaking remains flat (in the supersymmetric limit) to all orders in $M^{-1}_{Planck}$. The grand unification scale arises from an interplay of the Planck and supersymmetry breaking scales. An `internal' $Z_3\otimes Z_4$ symmetry protects a pair of electroweak doublets from becoming superheavy, yielding at the same time the supersymmetric `$\mu$ term' with the right order of magnitude. The $Z_4$ symmetry also acts as matter parity and eliminates the dangerous baryon number violating couplings.