# C. Castro: A Clifford Algebra Based Grand Unification Program of Gravity and the Standard Model : A Review Study

Carlos Castro, 70 Pages. Submitted to Int. J. Mod. Phys. A.

Abstract.
A Clifford $Cl ( 5, C )$ Unified Gauge Field Theory formulation of Conformal Gravity and $U (4 ) \times U ( 4 ) \times U(4)$ Yang-Mills in $4D$, is reviewed, along with its implications for the Pati-Salam group $SU (4) \times SU(2)_L \times SU(2)_R$, and $Trinification$ GUT models of $3$ fermion generations based on the group $SU (3)_C \times SU (3)_L \times SU(3)_R$. We proceed with a brief review of a unification program of $4D$ Gravity and $SU(3) \times SU (2) \times U (1)$ Yang-Mills emerging from $8D$ pure Quaternionic Gravity. A realization of $E_8$ in terms of the $Cl(16) = Cl (8) \otimes Cl(8)$ generators follows, as a preamble to Tony Smith’s $E_8$ and $Cl(16) = Cl(8) \otimes Cl(8)$ unification model in $8D$. The study of Chiral Fermions and Instanton Backgrounds in ${\bf CP}^2, {\bf CP}^3$ related to the problem of obtaining $3$ fermion generations is thoroughly studied. We continue with the evaluation of the coupling constants and particle masses based on the geometry of bounded complex homogeneous domains and geometric probability theory. An analysis of neutrino masses, Cabbibo-Kobayashi-Maskawa quark-mixing matrix parameters and neutrino-mixing matrix parameters follows. We finalize with some concluding remarks about other proposals for the unification of Gravity and the Standard Model, like string, $M, F$ theory and Noncommutative and Nonassociative Geometry.