Su(n) Susy Guts with String Remnants: Minimal Su(5) and Beyond

A new superstring-motivated framework for a treatment of SU(N) SUSY GUTs is argued. We show that all the present difficulties of the minimal supersymmetric SU(5) model can successfully be overcome with a new renormalizable reflection-invariant superpotential with two-adjoint scalars, one of which is interpreted as a massive string mode essentially decoupled from the low-energy particle spectra. This superpotential is proved to properly fix a mass ratio of the basic adjoint scalar moduli, while its gauge-type reflection symmetry essentially protects the model from gravitational smearing. The significant heavy threshold effect related with the generic mass splitting of adjoint moduli is shown to alter appropriately the running of gauge couplings towards the realistic string-scale grand unification. Furthermore, the extension of the superpotential to some SU(N) GUTs gives rise to, among many degenerate vacua, the missing VEV vacuum configuration for the basic adjoint scalar, thus providing a further clue to a doublet-triplet splitting problem, on the one hand, and a family symmetry SU(N −5)F for quarks and leptons, on the other. We predict the existence on a TeV scale two or three families of pseudo-Goldstone bosons of type (5 + 5̄) + SU(5)-singlets depending on SU(7) or SU(8) GUT selected. A talk given at XXIX International Conference on High Energy Physics, Vancouver, B.C., Canada, July 23-29, 1998.