A unification of left-right $\mathrm{SU}(3{)}_{\mathrm{L}}\times \mathrm{SU}(3{)}_{\mathrm{R}}$, color $\mathrm{SU}(3{)}_{\mathrm{C}}$, and family $\mathrm{SU}(3{)}_{\mathrm{F}}$ symmetries in a maximal rank-8 subgroup of ${\mathrm{E}}_8$ 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 ${[\mathrm{SU}(3)]}^3$ and global $\mathrm{SU}(3{)}_{\mathrm{F}}$-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 $\mu$ 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 ${\mathrm{E}}_6$ $\mathbf{27}$-plet per generation as well as three gauge and one family SU(3) octets inspired by the fundamental sector of ${\mathrm{E}}_8$. The details of the corresponding (SUSY and gauge) symmetry-breaking scheme, multiscale gauge couplings’ evolution, and resulting effective low-energy scenarios are discussed.

• Received 26 July 2018

DOI:https://doi.org/10.1103/PhysRevD.99.035041

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Published by the American Physical Society