On the Unification of Conformal and Fuzzy Gravities with $SO(10)$ GUT

TL;DR

The paper develops a gauge-theoretic route to unifying gravity with internal gauge interactions by enlarging the tangent-space symmetry. It constructs Conformal Gravity as a gauge theory of $SO(2,4)$ with spontaneous breaking to either Einstein gravity or Weyl gravity, and extends the framework to noncommutative (Fuzzy) Gravity with a Snyder-inspired background, extending the gauge group to $SO(2,4)\times U(1)$. By promoting a unification through $SO(2,16)$ (or equivalently $SO(18)$) and appropriate symmetry-breaking chains, the authors obtain an $SO(10)$ GUT structure with four fermion families from spinor representations, and a parallel noncommutative construction for FG with internal interactions. The work argues that such a four-dimensional, gauge-theoretic unification is feasible, yielding concrete breaking patterns and low-energy effective actions that connect to the Palatini form of gravity and to GUT-scale physics, potentially informing phenomenology and model building in quantum gravity and beyond the Standard Model.

Abstract

Within the gauge-theoretic approach of gravity, the gauging of an enlarged symmetry of the tangent space in four dimensions allows gravity to be unified with internal interactions. We study the unification of the Conformal and Noncommutative (Fuzzy) Gravities with Internal Interactions based on the $SO(10)$ GUT.