Unification of Conformal Gravity and Internal Interactions

TL;DR

This paper proposes a unified gauge-theoretic framework for gravity and internal interactions by enlarging the tangent group to include both, enabling a consistent description of conformal gravity and its relation to Einstein gravity.

Contribution

It introduces an enlarged tangent group $SO(2,16)$ to unify gravitational and internal gauge interactions within a conformal gravity framework.

Findings

Unified description of gravity and internal interactions.

Inclusion of Weyl and Majorana conditions on fermions.

Potential to recover Einstein gravity via symmetry breaking.

Abstract

Based on the observation that the dimension of the tangent space is not necessarily equal to the dimension of the corresponding curved manifold and on the known fact that gravitational theories can be formulated in a gauge theoretic way, we discuss how to describe all known interactions in a unified manner. This is achieved by enlarging the tangent group of the four-dimensional manifold to $SO(2,16)$, which permits the inclusion of both gauge groups, the one that describes gravity as a gauge theory as well as the $SO(10)$ describing the internal interactions. Moreover it permits the use of both Weyl and Majorana conditions imposed on the fermions, as to avoid the duplication of fermion multiplets of $SO(10)$ appearing in previous attempts. The gravity theory discussed in the present work is the Conformal Gravity which, after a spontaneous symmetry breaking, can lead either to Weyl Gravity or to the usual Einstein Gravity.