Division Algebras and Supersymmetry I
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.
Keywords
Cite
@article{arxiv.0909.0551,
title = {Division Algebras and Supersymmetry I},
author = {John C. Baez and John Huerta},
journal= {arXiv preprint arXiv:0909.0551},
year = {2016}
}
Comments
16 pages, various errors corrected, new title. in Superstrings, Geometry, Topology, and C*-algebras, eds. R. Doran, G. Friedman and J. Rosenberg, Proc. Symp. Pure Math. 81, AMS, Providence, 2010, pp. 65-80