**The Exceptional E_8 Geometry of Clifford (16) Superspace and Conformal Gravity Yang-Mills Grand Unification**

by Carlos Castro

Center for Theoretical Studies of Physical Systems

Clark Atlanta University, Atlanta, GA. 30314, castro_at_ctps.cau.edu

June 2008

Submitted to: Int. Journal of Geom. Methods in Mod. Physics

**Abstract:** We continue to study the Chern-Simons E_8 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 E_8 Generalized

Yang-Mills (GYM) field theory, and is defined in the 15D boundary of a 16D bulk space. The Exceptional E_8 Geometry of the 256-dim slice of the 256 × 256-dimensional flat *Clifford*(16) space is explicitly constructed based on a spin connection \Omega^{AB}_M , that gauges the generalized Lorentz transformations in the tangent space of the 256-dim curved slice, and the 256 × 256 components of the vielbein field E^A_M, that gauge the nonabelian translations. Thus, in one-scoop, the vielbein E^A_M encodes *all* of the 248 E_8 generators and 8 additional nonabelian generalized translations associated with the *vectorial *parts of the generators of the diagonal subalgebra [ Cl ( 8 ) x Cl ( 8 )]_diagonal subalgebra of Cl (16). The generalized curvature, Ricci tensor, Ricci scalar, torsion and 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 E_8 -> E_7-> E_6, and performing a Kaluza-Klein-Batakis compactification on CP^2, 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.

**Keywords: **C-space Gravity, Clifford Algebras, Grand Unification, Exceptional algebras, String Theory.

**Source:**

C. Castro (email of 01/07/2008 23:43, revised: 02/07/2008 21:19 and 09/07/2008),

http://www.scribd.com/doc/3870934/E8-Geometry-of-Clifford-16-Superspace-GravityYangMills-GrandUnification

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