Division Algebras and Supersymmetry I
نویسندگان
چکیده
Supersymmetry is deeply related to division algebras. For example, 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.
منابع مشابه
Division Algebras and Supersymmetry
Supersymmetry is deeply related to division algebras. For example, 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...
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