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Three Generations and a Trio of Trialities

N. Furey
(
- Humboldt U., Berlin (main)
)
,
M.J. Hughes
(
- U. Leeds (main)
)

Sep 26, 2024

11 pages

e-Print:

2409.17948 [hep-ph]

Report number:

HU-EP-24/26

View in:

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Abstract: (arXiv)

We identify the Standard Model's

\mathfrak{su}(3)\oplus \mathfrak{su}(2)\oplus \mathfrak{u}(1)

internal symmetries within the triality symmetries

\mathfrak{tri}(\mathbb{C}) \oplus \mathfrak{tri}(\mathbb{H}) \oplus \mathfrak{tri}(\mathbb{O})

. From here, the corresponding Standard Model group action is applied to the triality triple

\left( \Psi_+, \Psi_-,V\right)

for

\Psi_+, \Psi_-, V \in \mathbb{C}\otimes\mathbb{H}\otimes\mathbb{O}

. Together,

\Psi_+

and

\Psi_-

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.

Note:

11 pages, 6 figures

References(54)

Figures(7)

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