Gravity model from (A)dS Yang-Mills theory

TL;DR

The paper proposes a one‑parameter Yang–Mills formulation for gravity based on the $(A)dS$ gauge group, with a contraction to the Poincaré group at $\alpha\to 0$ that preserves the action form while reinterpreting the gauge fields as tetrads and a Lorentz connection. It derives the Euler–Lagrange equations and shows that a consistent sector yields gravitational dynamics in first‑order form, including torsion that can be algebraically related to spin, and a metric emerging from tetrads. The approach naturally incorporates topological invariants that map to familiar gravitational terms such as Einstein–Palatini, Holst, Pontryagin, and Nieh–Yan, and it provides a mechanism (soldering via CGCT) by which diffeomorphisms arise from gauge transformations in the contracted theory. The work discusses implications for quantization, sign choices (SO(2,3) vs SO(1,4)), and connections to broader themes like the double copy, Higgs-like symmetry breaking, and renormalization group behavior of the theory.

Abstract

We investigate the relationship between a one-parameter family of (anti-)de Sitter Yang-Mills models and a model of Einstein-Palatini gravity with matter, realized through Inönu-Wigner contraction of the (A)dS algebra. By setting the group parameter $α$ to zero, the gauge transformation of the potential becomes consistent with the transformation properties of the tetrad form and spin connection. We show that a sector of the Yang-Mills dynamics exists in which the equations decouple. Moreover, a subset of the gauge transformations can be related to diffeomorphisms, leading to the identification of the tetrad field. Finally, the resulting dynamics is consistent with a gravitational dynamics in the first-order formalism.