A unification of left-right SU(3)L × SU(3)R, colour SU(3)C and family SU(3)F symmetries in a maximal rank-8 subgroup of E8 is proposed as a landmark for future explorations beyond the Standard Model (SM). We discuss the implications of this scheme in a supersymmetric (SUSY) model based on the trinification gauge [SU(3)] 3 and global SU(3)F family symmetries. Among the key properties of this model are the unification of SM Higgs and lepton sectors, a common Yukawa coupling for chiral fermions, the absence of the µ-problem, gauge couplings unification and proton stability to all orders in perturbation theory. The minimal field content consistent with a SM-like effective theory at low energies is composed of one E6 27-plet per generation as well as three gauge and one family SU(3) octets inspired by the fundamental sector of E8. The details of the corresponding (SUSY and gauge) symmetry breaking scheme, multi-scale gauge couplings' evolution, and resulting effective low-energy scenarios are discussed.

We present a supersymmetric (SUSY) model based on trinification ½SUð3Þ 3 and family SUð3Þ F symmetries embedded into a maximal subgroup of 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 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 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.

Two-Higgs-doublet models (2HDMs) with a flavored Uð1Þ 0 gauge symmetry are a popular extension to the Standard Model (SM), yet they currently lack a complete survey. In this paper, we present a full classification of anomaly-free 2HDMs within the SM fermion content, resulting in a total of 11 distinct models. Four of these are relatively well studied, while the rest either partially, or entirely, lack previous treatment. We study these textures under a variety of experimental bounds, focusing mainly on the previously unexplored models. This work is intended to act as a catalog to models worth considering in greater detail.

Despite the popularity of two-Higgs-doublet models (2HDMs) with a gauged Abelian flavor symmetry, the allowed Yukawa textures have only been partly explored so far. In this work, we classify and compare every anomaly-free instance, in the case of having two generations of right-handed neutrinos and a type-I seesaw mechanism. We found 16 valid implementations in total, out of which 11 agree well with current experimental bounds. To our knowledge, neither of these models have been considered previously.