Three-Dimensional Quantum Gravity Coupled to Gauge Fields

TL;DR

This paper explores the simulation of U(1) gauge fields coupled to 3D quantum gravity, analyzing the phase diagram and finding no evidence of phase transitions despite theoretical predictions.

Contribution

It introduces a method to simulate gauge fields with 3D quantum gravity and investigates the phase structure using numerical simulations.

Findings

Mean field theory predicts phase transitions between confined and deconfined phases.

Numerical simulations do not observe these predicted phase transitions.

The phase diagram remains inconclusive regarding the transition presence.

Abstract

We show how to simulate U(1) gauge fields coupled to three-dimensional quantum gravity and then examine the phase diagram of this system. Quenched mean field theory suggests that a transition separates confined and deconfined phases (for the gauge matter) in both the negative curvature phase and the positive curvature phase of the quantum gravity, but numerical simulations find no evidence for such transitions.