NSBL-EP-016 The SU5 Structure of 14-Dimensional Unification
In a 14-dimensional gravidynamic unification model, the spacetime as well as the internal symmetries of 2 lepton-quark generations would be consolidated in a 64-component Weyl fermion. Alternatively, the latter fermionic multiplet can describe 8 charged leptons, with 8 associated neutrinos, and the corresponding antiparticles. In such a framework, the dynamics of vector bosons, as well as of Higgs scalars, would be generated at the quantum level via unified couplings to a vector, an antisymmetric tensor of 3rd rank, and an antisymmetric tensor of 5th rank. We exhibit the complete SU5 structure of the latter couplings. The underlying SU5 would contain a color SU3 symmetry, in the case of the leptons and quarks, or a family SU3 symmetry, in the alternative model of purely leptonic unification. This work begins by writing the Lorentz algebra of 14 dimensional spacetime in terms of its 4-dimensional Lorentz subalgebra, and an internal O10 factor. The latter is expressed via its U5 subalgebra. The fermionic 64-plet is expressed in terms of 32 Weyl fermions in 4 dimensions.
Likewise, the pertinent vector and the tensors are expressed in terms of vectors and scalars in 4 dimensions. The emerging picture regarding the fundamental fermions, and their interactions, would lead to aspects that are describable by the O10 and SU5 unification models, whether the grand unified model of leptons and quarks, or the purely leptonic unification model.
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