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

TL;DR

This paper explores a level-1 affine Lie algebra extension of a8a7a8(8) with supersymmetry, proposing a unification framework for gauge couplings that could explain Standard Model features.

Contribution

It introduces a supersymmetric affine a8a7a8(8) level-1 algebra model that unifies gauge couplings and addresses flavor hierarchies.

Findings

Unifies three gauge couplings via affine a8a7a8(8) symmetry.

Incorporates a8a7a8(8) with a8a7a8(1) supersymmetry.

Supports a maximally symmetry breaking pattern.

Abstract

A flavor-unified theory based on the simple Lie algebra of ${\mathfrak{s}\mathfrak{u}}(8)$ 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 $\widehat{ \mathfrak{s}\mathfrak{u} }(8)_{ k_U =1}$ with the ${\cal N}=1$ supersymmetric extension is found to unify three gauge couplings through the maximally symmetry breaking pattern.