Particles as Wilson lines of gravitational field

TL;DR

The work reframes gravity with a nonzero cosmological constant as a gauge theory of $SO(4,1)$ formulated as a constrained BF theory, and shows that point particles can be realized as Wilson lines whose de Sitter charges encode mass and spin. By inserting localized symmetry-breaking Wilson lines and promoting a worldline Lorentz frame $\mathsf{h}(\tau)$, the authors derive particle dynamics that reproduce Mathisson–Papapetrou equations with torsion and yield Einstein equations with delta-function sources for $p^a$ and $s^{ab}$. In the quantum regime, particles correspond to Wilson lines in $SO(4,1)$ representations labeled by $(m,s)$, with a deformed amplitude when gravity is active, hinting at a spin-network interpretation. The framework offers a diffeomorphism-invariant path toward quantum gravity with matter, and a perturbative route in the gravitational coupling $\alpha$ that connects to insights from lower-dimensional gravity and topological sectors.

Abstract

Since the work of Mac-Dowell-Mansouri it is well known that gravity can be written as a gauge theory for the de Sitter group. In this paper we consider the coupling of this theory to the simplest gauge invariant observables that is, Wilson lines. The dynamics of these Wilson lines is shown to reproduce exactly the dynamics of relativistic particles coupled to gravity, the gauge charges carried by Wilson lines being the mass and spin of the particles. Insertion of Wilson lines breaks in a controlled manner the diffeomorphism symmetry of the theory and the gauge degree of freedom are transmuted to particles degree of freedom.