Safe trinification

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 vectorlike 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 top, Higgs, bottom, and tau masses are recovered, we find the set of allowed solutions to be quite restrictive. Furthermore, we find there exists a lower bound of about 10 TeV for the symmetry breaking scale, making this model vulnerable to experiment.