Abstract
In the context of E6 Grand Unified Theories (GUTs), an intriguing possibility for symmetry breaking to the Standard Model (SM) group involves an intermediate stage characterized by either SU(3) × SU(3) × SU(3) (trinification) or SU(6) × SU(2). The more common choices of SU(5) and SO(10) GUT symmetry groups do not offer such breaking chains. We argue that the presence of a real (rank 2 tensor) representation 650 of E6 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 650 and find vacuum solutions that support regularly embedded subgroups SU(3) × SU(3) × SU(3), SU(6) × SU(2), and SO(10) × U(1), as well as specially embedded subgroups F4 and SU(3) × G2 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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Acknowledgments
The work of KSB is supported in part by the U.S. Department of Energy under grant number DE-SC0016013. BB acknowledges the financial support from the Slovenian Research Agency (research core funding No. P1-0035 and in part research grant J1-4389). VS acknowledges financial support from the Grant Agency of the Czech Republic (GAČR) via Contract No. 20-17490S, as well as from the Charles University Research Center Grant No. UNCE/SCI/013. We thank Raymond Volkas for discussion and pointing out ref. [21].
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Babu, K.S., Bajc, B. & Susič, V. Trinification from E6 symmetry breaking. J. High Energ. Phys. 2023, 11 (2023). https://doi.org/10.1007/JHEP07(2023)011
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DOI: https://doi.org/10.1007/JHEP07(2023)011