Quantum Gravity and String Theory


RxCxHxO-valued Gravity as a Grand Unified Field Theory

Authors: Carlos Castro

It is argued 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, it leads to a $[SU(4)]^4$ symmetry group revealing the possibility of extending the standard model by introducing additional gauge bosons, heavy quarks and leptons, and an extra $fourth$ family of fermions. We finalize by displaying the analog of the Einstein-Hilbert action for ${\bf R} \otimes {\bf C} \otimes {\bf H} \otimes {\bf O}$-valued gravity via the use of matrices, and which is based on ``coloring" the graviton; i.e. by attaching internal indices to the metric $g_{\mu \nu}$. In the most general case, $U(16)$ arises as the isometry group, while $U(8)$ is the isometry group in the split-octonion case.

Comments: 22 Pages. Submitted to Advances in Applied Clifford Algebras

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Submission history

[v1] 2018-08-14 08:40:38
[v2] 2018-08-19 03:22:19
[v3] 2018-11-22 06:41:46

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