Octonions, superstrings and ten-dimensional spinors

Abstract

A connection between the group/spin(8) and octonions is investigated and on this basis of octonions the algebra which faithfully represents spin(8) is constructed. This octonion algebra is used to describe the superstring theory. Furthermore, using these spin(8)-covariant octonions, we construct the ten-dimensional space-time octonionic spinors together with finite spinor transformations. In the ten-dimensional spacetime, the octonionic forms of Dirac equations, the action of a supersymmetric Yang-Mills field and the super symmetry transformations are introduced.