The unification in an $\widehat{\mathfrak{su}}(8{)}_{k_U=1}$ affine Lie algebra

Abstract

A flavor-unified theory based on the simple Lie algebra of $\mathfrak{su}(8)$ was previously proposed to generate the observed Standard Model quark/lepton mass hierarchies and the Cabibbo-Kobayashi-Maskawa mixing pattern due to their non-universal symmetry properties. A level-$1$ affine Lie algebra of $\widehat{\mathfrak{su}}(8{)}_{k_U=1}$ with the $\mathcal{N}=1$ supersymmetric extension is found to unify three gauge couplings through the maximally symmetry breaking pattern.

Comments: 27 pages with references, two appendices, 4 tables, 3 figures. Sequel to: arXiv:2307.07921, arXiv:2402.10471, arXiv:2406.09970, arXiv:2409.03172, matches the published version