Abstract
A unification of left-right $\rm{SU}(3)_\rm{L}\times \rm{SU}(3)_\rm{R}$, colour $\rm{SU}(3)_\rm{C}$ and family $\rm{SU}(3)_\rm{F}$ symmetries in a maximal rank-8 subgroup of ${\rm{E}}_8$ 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 $\left[\rm{SU}(3)\right]^3$ and global $\rm{SU}(3)_\rm{F}$ 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 $\mathrm{E}_6$ $27$-plet per generation as well as three gauge and one family $\rm{SU}(3)$ octets inspired by the fundamental sector of ${\rm{E}}_8$. The details of the corresponding (SUSY and gauge) symmetry breaking scheme, multi-scale gauge couplings' evolution, and resulting effective low-energy scenarios are discussed.
Highlights
Finding successful candidate theories unifying the strong and electroweak interactions, leading to a detailed understanding of the Standard Model (SM) origin, with all its parameters, hierarchies, symmetries, and particle content remains a big challenge for the theoretical physics community
We would like to summarize the basic features of the left-right-color-family (LRCF)-symmetric SUSY Higgs-unified trinification (SHUT) theory considered in this paper: (1) In contrast to previous grand-unified theories (GUTs)-scale formulations based on gauge trinification, all three fermion generations are unified into a single (27, 3)-plet of SUð3ÞF × E6, and no copies of any fundamental E6 representations are required for its consistent breaking down to the gauge symmetry of the SM
The considered SUð3ÞF × E6 symmetry can be embedded into E8, motivating the addition of ð1; 8Þ and ð78; 1Þ multiplets corresponding to four SU(3)-octet representations
Summary
Finding successful candidate theories unifying the strong and electroweak interactions, leading to a detailed understanding of the Standard Model (SM) origin, with all its parameters, hierarchies, symmetries, and particle content remains a big challenge for the theoretical physics community. The model has a particular feature in that no further spontaneous breaking of the symmetry towards the SM gauge group is provided by the SUSY conserving part of the model and that the energy scales at which the symmetry is further broken are instead associated with the soft SUSY-breaking operators. As such, both the electroweak scale and the scales of intermediate symmetry breaking are naturally suppressed relative to the GUT scale. The scalar components of chiral supermultiplets and fermionic components of vector supermultiplets carry a tilde (e.g., Δ ), except for the HiggsHiggsino sector where the tilde serves to identify the fermion SUð2ÞL × SUð2ÞR bidoublets (e.g., H ). (2) Fundamental representations carry superscript indices, while antifundamental representations carry subscript indices. (3) SUð3ÞK and SUð2ÞK (anti-)fundamental indices are denoted by k; k0; k1; k2... for K 1⁄4 L, R, respectively, while color indices are denoted by x; x0; x1; x2.... (4) Indices belonging to (anti-)fundamental representations of SUð3ÞF are denoted by i; j; k.... (5) If a field transforms both under gauge and global symmetry groups, the index corresponding to the global one is placed within the parentheses around the field, while the indices corresponding to the gauge symmetries are placed outside. (6) Global symmetry groups will be indicated by f...g
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