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

TL;DR

This paper introduces a supersymmetric trinification model embedded in E8, unifying Higgs and leptons, and enabling symmetry breaking to a left-right symmetric theory while maintaining gauge unification and proton stability.

Contribution

It presents a novel E8-embedded SUSY trinification model that unifies Higgs and leptons and offers a new pathway for symmetry breaking and unification.

Findings

Unifies Higgs and leptons into a single supermultiplet.

Enables symmetry breaking to a left-right symmetric theory.

Ensures gauge and Yukawa coupling unification, proton stability.

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.