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.

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

References in corpus (4)

• Doubly Lopsided Mass Matrices from Unitary Unification
• The global $B-L$ symmetry in the flavor-unified $\mathrm{SU}(N)$ theories
• The Standard Model quark/lepton masses and the Cabibbo-Kobayashi-Maskawa mixing in an $\mathrm{SU}(8)$ theory
• The gauge coupling evolutions of an $\mathrm{SU}(8)$ theory with the maximally symmetry breaking pattern

Cited by in corpus (2)

• Further study of the maximally symmetry breaking patterns in an $\mathrm{SU}(8)$ theory
• The non-topological $Z^{\prime }$ string in the 331 model and its classical stability