On Unification of Gravity and Gauge Interactions

TL;DR

This paper proposes a unification of gravity and gauge interactions through a higher-dimensional Lorentz group, specifically using the spin connection to encompass both forces within a single geometric framework.

Contribution

It introduces a model where the gauged Lorentz group unifies gravity and gauge fields, leading to a natural incorporation of grand unified theories within a higher-dimensional Lorentz symmetry.

Findings

Unification of gravity and gauge interactions via higher-dimensional Lorentz groups.

Identification of $SO(1,13)$ as a realistic unification group including all known particles.

Mechanism for giving mass to mirror fermions using topological superconductor techniques.

Abstract

Considering a higher dimensional Lorentz group as the tangent symmetry, 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. Mirror fermions could acquire mass utilizing a mechanism employed for topological superconductors. Family unification could be achieved by considering the $SO(1,21)$ Lorentz group.