We present phenomenologically viable SU(5) unified models which are finite to all orders before the spontaneous symmetry breaking. In the case of two models with three families the top quark mass is predicted to be 178.8 GeV.MPI-Ph/92-70

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Perturbative unification of soft supersymmetry-breaking (SSB) parameters is proposed in Gauge-Yukawa unified models. The method, which can be applied in any finite order in perturbation theory, consists in searching for renormalization group invariant relations among the SSB parameters, which are consistent with perturbative renormalizability. For the minimal Gauge-Yukawa unified model based on SU(5) we find that the low energy SSB sector contains a single arbitrary parameter, the unified gaugino mass. Within a certain approximation we find that the model predicts a superpartner spectrum which is consistent with the experimental data.

Gauge-Yukawa Unification (GYU) is obtained in GUTs by searching for renormalization group invariant relations among gauge and Yukawa couplings beyond the unification scale. Of particular interest are two supersymmetric GUTs, the finite and the minimal SU (5) models. Both models provided us,among others,with predictions of the top quark mass which so far have passed successfully the tests of progressively more accurate measurements.

1, 1, . . . , N ) as candidates for the unification symmetry of all particles. In particular we examine to which extent such theories can become finite and we find that a necessary condition is that there should be exactly three families. We discuss further some phenomenological issues related to the cases (N, k) = (3, 3), (3, 4), and (4, 3), in an attempt to choose those theories that can become also realistic. Thus we are naturally led to consider the SU(3) 3 model which we first promote to an all-loop finite theory and then we study its additional predictions concerning the top quark mass, Higgs mass and supersymmetric spectrum.