Standard model and gravity from spinors
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It is shown how the Lorentz and standard-model gauge groups can be unified by using algebraic spinors of the standard four-dimensional Clifford algebra, in left–right symmetric fashion. This defines a framework of unification with gravity and generates exactly a standard-model family of fermions, while a Pati–Salam unification group emerges, at the Planck scale, where (chiral) gravity decouples. We show that this low-energy broken phase emerges from the VEV of extended vierbein fields, which at this stage are assumed to be dynamically generated from a theory in the fully symmetric phase valid beyond the Planck scale (and whose consistency and dynamics is thus yet to be assessed) providing thus a geometrical and group-theoretical framework for the unification and breaking. At low energy, on the other hand, it is intriguing to find, as a remnant of this unification, new isospin-triplet spin-two particles that may naturally lie at the weak scale, providing a striking signal at the LHC.
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