The Standard Model gauge group is characterized as a subgroup of Spin(10) via two suitably aligned commuting complex structures on R^10 encoded in orthogonal pure spinors whose sum is pure, described efficiently with octonions.
(1,9)-spacetime --> (1,3)-spacetime: Reduction => U(1)xSU(2)xSU(3)
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abstract
A derivation of the standard symmetry and leptoquark family structure is presented that is more straightforward than a previous derivation.
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2025 1verdicts
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Octonions, complex structures and Standard Model fermions
The Standard Model gauge group is characterized as a subgroup of Spin(10) via two suitably aligned commuting complex structures on R^10 encoded in orthogonal pure spinors whose sum is pure, described efficiently with octonions.