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Further study of the maximally symmetry breaking patterns in an SU(8) theory

Ning Chen*, Zhiyuan Chen†, Zhanpeng Hou‡, Zhaolong Teng§, and Bin Wang∥

  • *Contact author: chenning_symmetry@nankai.edu.cn
  • †Contact author: chenzhiyuan@mail.nankai.edu.cn
  • ‡Contact author: houzhanpeng@mail.nankai.edu.cn
  • §Contact author: tengcl@mail.nankai.edu.cn
  • ∥Contact author: wb@mail.nankai.edu.cn
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Phys. Rev. D 111, 115034 – Published 26 June, 2025

DOI: https://doi.org/10.1103/wsm5-xfzt

Abstract

An SU(8) theory was previously found to be the minimal simple gauge group where all three-generational Standard Model (SM) fermions can be nontrivially embedded. It is maximally broken into a subgroup of SU(8)→G441≡SU(4)s⊗SU(4)W⊗U(1)X0 at the grand unified theory scale by the SU(8) adjoint Higgs field of 63H. Gauge symmetries in the strong and the weak sectors are extended by one and two ranks, respectively. The sequential strong-weak-weak (SWW) symmetry breaking stages were found to generate the observed hierarchical SM quark/lepton masses as well as the Cabibbo-Kobayashi-Maskawa mixing pattern with the precise flavor identifications [The global B− L symmetry in the flavor-unified SU(N) theories, J. High Energy Phys. 04 (2024) 046. and The standard model quark/lepton masses and the Cabibbo-Kobayashi-Maskawa mixing in an SU(8) theory, J. High Energy Phys. 12 (2024) 137.]. We further study the possible weak-strong-weak and weak-weak-strong symmetry breaking patterns and compare with the results that we have obtained by following the SWW sequence. The two-loop renormalization group equations following both patterns are analyzed, where we cannot achieve the gauge coupling unification in the field theory framework. Through these analyses, we suggest the gauge coupling unification to be interpreted in the context of the affine Lie algebra.

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Phys. Rev. D 111, 115034– Published 26 June, 2025
  • Received 25 November 2024
  • Accepted 4 June 2025
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