## The Clifford Space Geometry of Conformal Gravity and U(4) X U(4) Yang-Mills Unification

**Authors:** Carlos Castro

It is shown how a Conformal Gravity and U(4) X U(4) Yang-Mills Grand Unification
model in four dimensions can be attained from a Clifford Gauge Field
Theory in C-spaces (Clifford spaces) based on the (complex) Clifford Cl(4,C) algebra
underlying a complexified four dimensional spacetime (8 real dimensions).
Upon taking a real slice, and after symmetry breaking, it leads to ordinary Gravity
and the Standard Model in four real dimensions. A brief conclusion about
the Noncommutative star product deformations of this Grand Unified Theory
of Gravity with the other forces of Nature is presented.

**Comments:** 22 pages, This article will appear in the Int J. of Mod. Phys A.

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### Submission history

[v1] 21 Aug 2009

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