Eur. Phys. J. C (2009) 59: 723-729
https://doi.org/10.1140/epjc/s10052-008-0808-y

Regular Article - Theoretical Physics

Standard model and gravity from spinors

University of L’Aquila & INFN–LNGS, 67100, L’Aquila, Italy

^* e-mail: nesti@aquila.infn.it

Received: 30 September 2008
Revised: 5 November 2008
Published online: 26 November 2008

Abstract

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.