Quantum Gravity and String Theory


C x H x O-valued Gravity, [SU(4)]$^4$ Unification, Hermitian Matrix Geometry and Nonsymmetric Kaluza-Klein Theory

Authors: Carlos Castro

We review briefly how {\bf R} $\otimes$ {\bf C} $\otimes$ {\bf H} $\otimes$ {\bf O}-valued Gravity (real-complex-quaterno-octonionic Gravity) naturally can describe a grand unified field theory of Einstein's gravity with a Yang-Mills theory containing the Standard Model group $SU(3) \times SU(2) \times U(1)$. In particular, the $ C \otimes H \otimes O$ algebra is explored deeper. It is found that it can furnish the gauge group {\bf [SU(4)]}$^4$ revealing the possibility of extending the Standard Model by introducing additional gauge bosons, heavy quarks and leptons, and a $fourth$ family of fermions with profound physical implications. An analysis of $ C \otimes H \otimes O$-valued gravity reveals that it bears a connection to Nonsymmetric Kaluza-Klein theories and complex Hermitian Matrix Geometry. The key behind these connections is in finding the relation between $ C \otimes H \otimes O$-valued metrics in $two$ $complex$ dimensions with metrics in $higher$ dimensional $real$ manifolds ($ D = 32 $ real dimensions in particular). It is desirable to extend these results to hypercomplex, quaternionic manifolds and Exceptional Jordan Matrix Models.

Comments: 15 Pages. Submitted to Advances in Applied Clifford Algebras

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Submission history

[v1] 2018-11-07 03:15:29

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