Unifying Gravities with Internal Interactions

TL;DR

The paper investigates a gauge-theoretic route to unifying gravity with internal interactions by leveraging the mismatch between tangent-group and manifold dimensions, formulating gravity as a gauge theory of enlarged groups. It shows how conformal gravity can be realized as an $SO(2,4)$ gauge theory and broken either to Einstein gravity or Weyl gravity via two distinct symmetry-breaking paths, and extends the framework to noncommutative (fuzzy) gravity by promoting to $SO(2,4)\times U(1)$ with a scalar in the antisymmetric sector. Building on this, it proposes an $SO(2,16)$ unification that embeds gravity and $SO(10)$-type internal interactions, with fermions in suitable bi-fundamental representations yielding chiral families after symmetry breaking; the construction recovers a Palatini form with a cosmological constant in the commutative limit and indicates four-family spectra at low energies. Overall, the work provides a cohesive, gauge-based foundation for gravitation and internal symmetries, opening pathways to phenomenology through symmetry-breaking scales and potential gravitational-wave or cosmological signatures.

Abstract

Reviving the old proposal of describing gravity as a gauge theory first we describe the construction of the Conformal and the Noncommutative (Fuzzy) Gravities in a gauge-theoretic manner. Then stressing the fact that the tangent group of a curved manifold and the manifold itself do not necessarily have the same dimensions, we show how the above Gravities can be unified with the Internal Interactions, the latter based on the GUT $SO(10)$.