Reviving trinification models through an $\mathrm{E}_6$-extended supersymmetric GUT

Abstract

We present a supersymmetric (SUSY) model based on trinification $[\mathrm{SU}(3)]^3$ and family $\mathrm{SU}(3)_\mathrm{F}$ symmetries embedded into a maximal subgroup of $\mathrm{E}_8$, where the sectors of light Higgs bosons and leptons are unified into a single chiral supermultiplet. The common origin of gauge trinification and of the family symmetry from $\mathrm{E}_8$ separates the model from other trinification-based GUTs, as it protects, in particular, the Standard Model fermions from gaining mass until the electroweak symmetry is broken. Furthermore, it allows us to break the trinification symmetry via vacuum expectation values in $\mathrm{SU}(3)$-adjoint scalars down to a left-right symmetric theory. Simultaneously, it ensures the unification of the gauge and Yukawa couplings as well as proton stability. Although the low-energy regime (e.g. mass hierarchies in the scalar sector determined by a soft SUSY-breaking mechanism) is yet to be established, these features are one key to revive the once very popular trinification-based GUTs.