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An octonionic formulation of the M-theory algebra

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arxiv 1402.4649 v1 pith:FHLEIHR6 submitted 2014-02-19 hep-th math-phmath.MP

A. Anastasiou , L. Borsten , M. J. Duff , L. J. Hughes , S. Nagy This is my paper · ORCID
classification hep-thmath-phmath.MP
keywords algebradivisionoctonionicformulationlinearproductsupersymmetryterms
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We give an octonionic formulation of the N = 1 supersymmetry algebra in D = 11, including all brane charges. We write this in terms of a novel outer product, which takes a pair of elements of the division algebra A and returns a real linear operator on A. More generally, with this product comes the power to rewrite any linear operation on R^n (n = 1,2,4,8) in terms of multiplication in the n-dimensional division algebra A. Finally, we consider the reinterpretation of the D = 11 supersymmetry algebra as an octonionic algebra in D = 4 and the truncation to division subalgebras.

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  1. The Unified Standard Model

    hep-th 2019-09 conditional novelty 6.0 of 10

    All Standard Model particle types and the SU(3)xSU(2)xU(1) gauge structure are placed inside the matrix algebra M(8,C), built from the octonions, with two leftover states.

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