On unification of gravity and gauge interactions

Abstract

Abstract: Considering a higher dimensional Lorentz group as the symmetry of the tangent space, we unify gravity and gauge interactions in a natural way. The spin connection of the gauged Lorentz group is then responsible for both gravity and gauge fields, and the action for the gauged fields becomes part of the spin curvature squared. The realistic group which unifies all known particles and interactions is the SO(1, 13) Lorentz group whose gauge part leads to SO(10) grand unified theory and contains double the number of required fermions in the fundamental spinor representation. We briefly discuss the Brout-Englert-Higgs mechanism which breaks the SO(1, 13) symmetry first to SO(1, 3) × SU(3) × SU(2) × U(1) and further to SO(1, 3) × SU(3) × U(1) and gives very heavy masses to half of the fermions leaving the others with light masses.