Nonmaximal symmetry breaking patterns in the supersymmetric $\widehat{\mathfrak{su}}(8{)}_{k_U=1}$ theory

Abstract

We study the nonmaximal symmetry breaking patterns of $\mathfrak{su}(8)\to {\mathfrak{g}}_{531}/{\mathfrak{g}}_{351}$ allowed in a supersymmetric theory with the affine Lie algebra of $\widehat{\mathfrak{su}}(8{)}_{k_U=1}$, which was recently proposed to explain the three-generational standard model quark/lepton mass hierarchies as well as the Cabbibo-Kobayashi-Maskawa mixing pattern. Three gauge couplings are found to achieve the unification below the Planck scales, according to the unification relations determined by the affine Lie algebra at level of $1$. We also prove that a separate nonmaximal symmetry breaking pattern of $\mathfrak{su}(8)\to {\mathfrak{g}}_{621}$ is unrealistic due to the additional massless vectorlike quarks in the spectrum.

Comments: 30 pages with references, one appendices, 15 tables. Sequel to: arXiv:2307.07921, arXiv:2402.10471, arXiv:2406.09970, arXiv:2409.03172, arXiv:2411.12979