Safe Trinification

In this work, we provide a UV safe Trinification theory in which the Standard Model is embedded. Using recently developed large number-of-flavor techniques, safety is achieved by adding to the theory gauged vector-like fermions. We find that all gauge, scalar quartic, and Yukawa couplings achieve an interacting ultraviolet fixed point below the Planck scale. We find renormalization group flow solutions matching the Standard Model in the IR, indicating a truly UV completion of the Standard Model. Imposing constraints that realistic Higgs, top, bottom, tau and reasonable neutrino masses are recovered, we find the set of allowed solutions to be quite restrictive. Furthermore, the symmetry breaking scale is predicted to be around 10 TeV, making this model vulnerable to experiment.