Unification of Gravity and Internal Interactions

Abstract

In the gauge theoretic approach of gravity, General Relativity is described by gauging the symmetry of the tangent manifold in four dimensions. Usually the dimension of the tangent space is considered to be equal to the dimension of the curved manifold. However, the tangent group of a manifold of dimension $d$ is not necessarily $SO_d$. It has been suggested earlier that by gauging an enlarged symmetry of the tangent space in four dimensions one could unify gravity with internal interactions. Here we consider such a unified model by gauging the $SO_{(1,17)}$ as the extended Lorentz group overcoming in this way some difficulties of the previous attempts of similar unification and eventually we obtain the $SO_{10}$ GUT, supplemented by an $SU_2 \times SU_2$ global symmetry.