Wilson loops in CDT quantum gravity

TL;DR

This paper introduces a method to measure gravitational holonomies and Wilson loops in lattice quantum gravity, revealing that these holonomies uniformly cover the SO(4) group manifold, advancing understanding of quantum geometric properties.

Contribution

It provides a simple construction for Wilson loops in CDT quantum gravity and analyzes their properties, offering new tools for nonperturbative quantum gravity studies.

Findings

Holonomies cover the SO(4) group manifold uniformly

Wilson line observables can be explicitly constructed and measured

The approach links quantum gravity with gauge theory concepts

Abstract

By explicit construction, we show that one can in a simple way introduce and measure gravitational holonomies and Wilson loops in lattice formulations of nonperturbative quantum gravity based on (Causal) Dynamical Triangulations. We use this set-up to investigate a class of Wilson line observables associated with the world line of a point particle coupled to quantum gravity, and deduce from their expectation values that the underlying holonomies cover the group manifold of SO(4) uniformly