4D Quantum Gravity Coupled to Matter

TL;DR

This study explores the phase structure of 4D quantum gravity coupled with matter fields using numerical simulations, revealing weak coupling away from criticality and persistent phase transitions unaffected by matter inclusion.

Contribution

It provides the first numerical analysis of matter coupling effects on 4D quantum gravity phase transitions using simplicial manifold models.

Findings

Weak matter-geometry coupling away from critical point

Clear coupling at Ising critical point

Phase transition remains unchanged with matter inclusion

Abstract

We investigate the phase structure of four-dimensional quantum gravity coupled to Ising spins or Gaussian scalar fields by means of numerical simulations. The quantum gravity part is modelled by the summation over random simplicial manifolds, and the matter fields are located in the center of the 4-simplices, which constitute the building blocks of the manifolds. We find that the coupling between spin and geometry is weak away from the critical point of the Ising model. At the critical point there is clear coupling, which qualitatively agrees with that of gaussian fields coupled to gravity. In the case of pure gravity a transition between a phase with highly connected geometry and a phase with very ``dilute'' geometry has been observed earlier. The nature of this transition seems unaltered when matter fields are included. It was the hope that continuum physics could be extracted at the transition between the two types of geometries. The coupling to matter fields, at least in the form discussed in this paper, seems not to improve the scaling of the curvature at the transition point.