Beyond the Standard Model with Six-Dimensional Spinors

Abstract

Six-dimensional spinors with Spin(3,3) symmetry are utilized to efficiently encode three generations of matter. E8(−24) is shown to contain physically relevant subgroups with representations for GUT groups, spacetime symmetries, three generations of the standard model fermions, and Higgs bosons. Pati–Salam, SU(5), and Spin(10) grand unified theories are found when a single generation is isolated. For spacetime symmetries, Spin(4,2) may be used for conformal symmetry, AdS5→dS4, or simply broken to Spin(3,1) of a Minkowski space. Another class of representations finds Spin(2,2) and can give AdS3 with various GUTs. An action for three generations of fermions in the Majorana–Weyl spinor 128 of Spin(4,12) is found with Spin(3) flavor symmetry inside E8(−24). The 128 of Spin(12,4) can be regarded as the tangent space to a particular pseudo-Riemannian form of the octo-octonionic Rosenfeld projective plane E8(−24)/Spin(12,4)=(OsxO)P2.