SU(3)xSU(2)xU(1), Higgs, and Gravity from Spin(0,8) Clifford Algebra Cl(0,8)
The Lagrangian action for the D4-D5-E6 model of hep-th/9306011 has 8-dim spacetime V8 of the vector representation of Spin(0,8); 8-dim fermion fields S8+ = S8- of the half-spinor reps of Spin(0,8); and 28 gauge boson fields of the bivector adjoint rep of Spin(0,8). In this paper, the structure of the positive definite Clifford algebra Cl(0,8) of Spin(0,8), and the triality automorphism V8 = S8+ = S8-, are used to reduce the spacetime to 4 dimensions and thereby change the gauge group from Spin(0,8) to the realistic SU(3)xSU(2)xU(1), Higgs, and Gravity. The effect of dimensional reduction on fermions, to introduce 3 generations, has been described in hep-ph/9301210. The global geometry of manifolds V8 = S8+ = S8- = RP1xS7, the effects of dimensional reduction on them, and the calculation of force strength constants, has been described in hep-th/9302030.