R ⊗ C ⊗ H ⊗ O-Valued Gravity as a Grand Unified Field Theory

Abstract:

It is argued how R⊗ C⊗ H⊗ 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) × SU(2) × 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 R⊗ C⊗ H⊗ 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 gμν. In the most general case, U(16) arises as the isometry group, while U(8) is the isometry group in the split-octonion case.

Año de publicación:

2019

Keywords:

• Nonassociative Geometry
• Unification
• Quaternions
• strings
• Octonionic Gravity
• Clifford algebras

Fuente:

scopus