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Octions: An $E_8$ description of the Standard Model

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arxiv 2204.05310 v2 pith:OQPXNRPH submitted 2022-04-11 hep-ph hep-th

Corinne A. Manogue , Tevian Dray , Robert A. Wilson This is my paper · ORCID
classification hep-phhep-th
keywords mathfrakalgebramodelstandardelementsspinorsthentimes
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abstract

We interpret the elements of the exceptional Lie algebra $\mathfrak{e}_{8(-24)}$ as objects in the Standard Model, including lepton and quark spinors with the usual properties, the Standard Model Lie algebra $\mathfrak{su}(3)+\mathfrak{su}(2)+\mathfrak{u}(1)$, and the Lorentz Lie algebra $\mathfrak{so}(3,1)$. Our construction relies on identifying a complex structure on spinors and then working in the enveloping algebra. The resulting model naturally contains GUTs based on $SO(10)$ (Georgi--Glashow), $SU(5)$ (Georgi), and $SU(4)\times SU(2)\times SU(2)$ (Pati--Salam). We then briefly speculate on the role of the remaining elements of $\mathfrak{e}_8$, and propose a mechanism leading to exactly three generations of particles.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Flipped $SU(5)$ GUT with conformal gravity from a single supermultiplet

    hep-th 2024-12 reject novelty 7.0 of 10

    A new superalgebra from the Grassmann envelope of E8(-24) is proposed as the origin of flipped SU(5) GUT plus conformal gravity, with three fermion generations and no superpartners.

  2. Standard Model Symmetries and the Nested Embeddings of $\mathbb{R}\subset\mathbb{C}\subset\mathbb{H}\subset\mathbb{O}$

    hep-ph 2026-07 conditional novelty 6.0 of 10

    The Standard Model gauge group and its charge operators emerge from O⊕H⊕C⊕R by stabilizing top-graded elements and imposing an equal-trace condition.

  3. The Dirac equation in (split-)octonions: origins, variants, and modern context

    math-ph 2026-06 conditional novelty 5.0 of 10

    Four approaches to the Dirac equation in (split-)octonions are classified; a 2024 split-octonionic equation is shown identical to the 2006 2-factor form by structure-preserving rotation and relabeling.

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