Division algebras and supersymmetry Export

@article{citeulike:5720797, 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.}, archivePrefix = {arXiv}, author = {Baez, John C. and Huerta, John}, citeulike-article-id = {5720797}, citeulike-linkout-0 = {http://arxiv.org/abs/0909.0551}, citeulike-linkout-1 = {http://arxiv.org/pdf/0909.0551}, day = {2}, eprint = {0909.0551}, keywords = {division\_algebras, susy}, month = {Sep}, posted-at = {2009-09-05 19:36:22}, priority = {2}, title = {Division algebras and supersymmetry}, url = {http://arxiv.org/abs/0909.0551}, year = {2009} }

TY - JOUR ID - citeulike:5720797 L3 - citeulike-article-id:5720797 N2 - 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. TI - Division algebras and supersymmetry KW - division_algebras KW - susy AU - Baez, John AU - Huerta, John PY - 2009/Sep/02/ UR - http://arxiv.org/abs/0909.0551 ER -