Carlos Castro Perelman – Valued Gravity as a Grand Unified Field Theory

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QGR Research Scientist Carlos Castro Perelman give a lecture on Valued Gravity as a Grand Unified Field Theory and argues how R ⊗ C ⊗ H ⊗ O-valued Gravity naturally can describe a grand unified field theory of Einstein’s gravity with an U (8) Yang-Mills theory. In particular, it allows for an extension of the Standard Model by including a 3-family SU (3)F symmetry group and an extra U (1) symmetry. A unification of left-right SU (3)L ×SU (3)R, color SU (3)C and family SU (3)F symmetries in a maximal rank-8 subgroup of E8 has been proposed by [33] as a landmark for future explorations beyond the Standard Model. It is warranted to explore further if this latter model also admits a similar gravitational interpretation based on the above composition of normed division algebras. Furthermore, our construction leads also to a bimetric theory of gravity which may have a role in dark energy. The crux of this approach is that we have replaced the Kaluza-Klein prescription to generate gauge symmetries in lower dimensions from isometries of the internal manifold, by U (8) isometry transformations of the R ⊗ C ⊗ H ⊗ O-valued metric.

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