## The Exceptional E_{8} Geometry of Clifford (16) Superspace and Conformal Gravity Yang-Mills Grand Unification

**Authors:** Carlos Castro

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 X 256-dimensional flat Clifford (16) space is explicitly constructed
based on a spin connection Ω_{M}^{AB}, 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 E_{M}^{A}, that gauge the nonabelian translations. Thus, in one-scoop, the vielbein
E_{M}^{A}
encodes all of the 248 (nonabelian) E_{8} 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 E_{8} ordinary Yang-Mills in 8D, after a sequence of symmetry
breaking processes E_{8} → E_{7} → E_{6} → SO(8, 2), 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.

**Comments:** 33 pages, This article appeared in the IJGMMP vol 6, no. 3 (2009) 385.

**Download:** **PDF**

### Submission history

[v1] 22 Aug 2009

**Unique-IP document downloads:** 285 times

**Add your own feedback and questions here:**

*You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.*

*
*