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.
@article{arxiv.hep-lat/9304016,
title = {Three-Dimensional Quantum Gravity Coupled to Gauge Fields},
author = {Ray L. Renken and Simon M. Catterall and John B. Kogut},
journal= {arXiv preprint arXiv:hep-lat/9304016},
year = {2009}
}