Unification based on the mysterious cubic-structure grouping of quarks and leptons

Abstract

We present a unification model based on the well-known but mysterious cubic-structure grouping of quarks and leptons that suggests an underlying symmetry connection deemed explainable by a unified theory. It results in an extension of the Pati-Salam model that consolidates the fermions into two sixteen-dimensional chiral representations of the gauge group. Moreover, the discrete cubic flavor symmetry arbitrarily conjectured in the literature is found here to be implied by the gauge symmetry. Furthermore, the gauge algebra also describes an eleven-dimensional spacetime decomposed into the usual spacetime and the seven-sphere, which is the manifold of unit octonions. This suggests such a spacetime is apt for embracing all elementary particles and their interactions.

arXiv commentTo appear in Physica Scripta 2023

References in corpus (17)

• Discrete Flavor Symmetries and Models of Neutrino Mixing
• Proton stability in grand unified theories, in strings, and in branes
• Neutrino Mixing and Quark-Lepton Complementarity
• Review of Lepton Universality tests in B decays
• Relation between the neutrino and quark mixing angles and grand unification
• S4 Flavor Symmetry and Fermion Masses: Towards a Grand Unified theory of Flavor
• Neutrino Mass Matrix from S_4 Symmetry
• Quantization and renormalization of the manifest left-right symmetric model of electroweak interactions
• S4 Flavor Symmetry of Quarks and Leptons in SU(5) GUT
• An SO(10) GUT Model with $S4$ Flavor Symmetry
• Non-Abelian Discrete Symmetries and Neutrino Masses: Two Examples
• Prospects for mass unification at low energy scales
• Division algebraic symmetry breaking
• Spin(11,3), particles and octonions
• The role of singletons in $S^7$ compactifications
• Why do elementary particles have such strange mass ratios? -- The role of quantum gravity at low energies
• Timelike duality, $M^{\prime }$-theory and an exotic form of the Englert solution