Critical Behavior of Dynamically Triangulated Quantum Gravity in Four Dimensions

TL;DR

This study investigates the phase transition in four-dimensional dynamical triangulation quantum gravity, revealing a continuum limit characterized by specific scaling laws and a Hausdorff dimension of 4 at criticality.

Contribution

It provides detailed analysis of the phase transition, including scaling behavior and Hausdorff dimension, supporting the existence of a continuum limit in 4D Euclidean quantum gravity.

Findings

Scaling laws observed near critical point

Hausdorff dimension reaches 4 at criticality

Curvature susceptibility diverges with index -0.6

Abstract

We performed detailed study of the phase transition region in Four Dimensional Simplicial Quantum Gravity, using the dynamical triangulation approach. The phase transition between the Gravity and Antigravity phases turned out to be asymmetrical, so that we observed the scaling laws only when the Newton constant approached the critical value from perturbative side. The curvature susceptibility diverges with the scaling index $-.6$. The physical (i.e. measured with heavy particle propagation) Hausdorff dimension of the manifolds, which is 2.3 in the Gravity phase and 4.6 in the Antigravity phase, turned out to be 4 at the critical point, within the measurement accuracy. These facts indicate the existence of the continuum limit in Four Dimensional Euclidean Quantum Gravity.