Three Generations and a Trio of Trialities

2024/09/26 by N. Furey, M. J. Hughes · 1 voice · 1 citation
Physics and Astronomy · #hep-ph #hep-th

paper · pdf · doi:10.1016/j.physletb.2025.139473

arxiv published 2024/09/26 · arxiv updated 2024/10/09

Abstract

We identify the Standard Model's \mathfraksu(3)⊕ \mathfraksu(2)⊕ \mathfraku(1) internal symmetries within the triality symmetries \mathfraktri(ℂ) ⊕ \mathfraktri(ℍ) ⊕ \mathfraktri(\mathbbO). From here, the corresponding Standard Model group action is applied to the triality triple ( Ψ₊, Ψ_-,V) for Ψ₊, Ψ_-, V ∈ ℂ⊗ℍ⊗\mathbbO. Together, Ψ₊ and Ψ_- provide the correct irreducible representations for two generations. Owing to a certain Cartan Factorization, which we define, V provides the irreducible representations for a third generation. Said more explicitly in another way, division algebraic multiplication merges a third generation of spinor representations into a set of scalar bosons. This set of scalar bosons includes the familiar Standard Model Higgs representation.

Cited by

• Higgs and Yukawa Structure in a Clifford Algebra Model with Three Generations and S₃ Family Symmetry
• Electroweak Structure and Three Fermion Generations in Clifford Algebra with S3 Family Symmetry

Discussions

• Bluesky academics, lets get to know each other! Quote this & tell me: 1) a project you are working on & 2) an odd idea/theory you aren’t working on but keep thinking about 1) The 3-generation proble [bsky, 2 points, 0 comments]

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