Gauge hierarchy, Planck scale corrections and the origin of GUT scale in supersymmetric (SU (3))³

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' Z₃ ⊗ Z₄ symmetry protects a pair of electroweak doublets from becoming superheavy, yielding at the same time the supersymmetric 'μ term' with the right order of magnitude. The Z₄ symmetry also acts as matter parity and eliminates the dangerous baryon number violating couplings.