Particles as Wilson lines of gravitational field

TL;DR

This paper demonstrates that Wilson lines in a gauge-theoretic formulation of gravity can model relativistic particles, with their mass and spin emerging as gauge charges, linking gauge invariants to particle dynamics.

Contribution

It introduces a novel approach where Wilson lines in a de Sitter gauge gravity theory reproduce particle dynamics, revealing a new connection between gauge invariants and matter.

Findings

Wilson lines reproduce relativistic particle dynamics

Gauge charges correspond to particle mass and spin

Diffeomorphism symmetry is broken by Wilson line insertion

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.