Division Algebras and Supersymmetry I

  title={Division Algebras and Supersymmetry I},
  author={John C. Baez and John Huerta},
  journal={arXiv: High Energy Physics - Theory},
  • J. Baez, J. Huerta
  • Published 2 September 2009
  • Mathematics
  • arXiv: High Energy Physics - Theory
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… 

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