Authors: Carlos Castro
We continue to study the Chern-Simons E8 Gauge theory of Gravity developed by the author which is a unified field theory (at the Planck scale) of a Lanczos-Lovelock Gravitational theory with a E8 Generalized Yang-Mills (GYM) field theory, and is defined in the 15D boundary of a 16D bulk space. The Exceptional E8 Geometry of the 256-dim slice of the 256 X 256-dimensional flat Clifford (16) space is explicitly constructed based on a spin connection ΩMAB, that gauges the generalized Lorentz transformations in the tangent space of the 256-dim curved slice, and the 256 X 256 components of the vielbein field EMA, that gauge the nonabelian translations. Thus, in one-scoop, the vielbein EMA encodes all of the 248 (nonabelian) E8 generators and 8 additional (abelian) translations associated with the vectorial parts of the generators of the diagonal subalgebra [Cl(8) ⊗ Cl(8)]diag ⊂ Cl(16). The generalized curvature, Ricci tensor, Ricci scalar, torsion, torsion vector and the Einstein-Hilbert-Cartan action is constructed. A preliminary analysis of how to construct a Clifford Superspace (that is far richer than ordinary superspace) based on orthogonal and symplectic Clifford algebras is presented. Finally, it is shown how an E8 ordinary Yang-Mills in 8D, after a sequence of symmetry breaking processes E8 → E7 → E6 → SO(8, 2), and performing a Kaluza-Klein-Batakis compactification on CP2, involving a nontrivial torsion, leads to a (Conformal) Gravity and Yang-Mills theory based on the Standard Model in 4D. The conclusion is devoted to explaining how Conformal (super) Gravity and (super) Yang-Mills theory in any dimension can be embedded into a (super) Clifford-algebra-valued gauge field theory.
Comments: 33 pages, This article appeared in the IJGMMP vol 6, no. 3 (2009) 385.
[v1] 22 Aug 2009
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