Division Algebras and Supersymmetry I

John C. Baez; John Huerta

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arXiv · 0909.0551

Division Algebras and Supersymmetry I

John C. Baez·John Huerta

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Abstract

Supersymmetry is deeply related to division algebras. Nonabelian Yang-Mills fields minimally coupled to massless spinors are supersymmetric if and only if the dimension of spacetime is 3, 4, 6 or 10. The same is true for the Green-Schwarz superstring. In both cases, supersymmetry relies on the vanishing of a certain trilinear expression involving a spinor field. The reason for this, in turn, is the existence of normed division algebras in dimensions 1, 2, 4 and 8: the real numbers, complex numbers, quaternions and octonions. Here we provide a self-contained account of how this works.

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John C. Baez, John Huerta. 2009-09-02. Division Algebras and Supersymmetry I. https://arxiv.org/abs/0909.0551

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