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arXiv · 2305.16398

Trinification from $\mathrm{E}_{6}$ symmetry breaking

K. S. Babu·Borut Bajc·Vasja Susič
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Abstract

In the context of $\mathrm{E}_{6}$ Grand Unified Theories (GUTs), an intriguing possibility for symmetry breaking to the Standard Model (SM) group involves an intermediate stage characterized by either $\mathrm{SU}(3)\times\mathrm{SU}(3)\times\mathrm{SU}(3)$ (trinification) or $\mathrm{SU}(6)\times\mathrm{SU}(2)$. The more common choices of $\mathrm{SU(5)}$ and $\mathrm{SO}(10)$ GUT symmetry groups do not offer such breaking chains. We argue that the presence of a real (rank $2$ tensor) representation $\mathbf{650}$ of $\mathrm{E}_{6}$ in the scalar sector is the minimal and likely only reasonable possibility to obtain one of the novel intermediate stages. We analyze the renormalizable scalar potential of a single copy of the $\mathbf{650}$ and find vacuum solutions that support regularly embedded subgroups $\mathrm{SU}(3)\times\mathrm{SU}(3)\times\mathrm{SU}(3)$, $\mathrm{SU}(6)\times\mathrm{SU}(2)$, and $\mathrm{SO}(10)\times\mathrm{U}(1)$, as well as specially embedded subgroups $\mathrm{F}_{4}$ and $\mathrm{SU}(3)\times\mathrm{G}_{2}$ that do not contain the SM gauge symmetry. We show that for a suitable choice of parameters, each of the regular cases can be obtained as the lowest among the analyzed minima in the potential.

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K. S. Babu, Borut Bajc, Vasja Susič. 2023-05-25. Trinification from $\mathrm{E}_{6}$ symmetry breaking. https://doi.org/10.1007/jhep07(2023)011

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