Euclidean Dynamical Triangulations Revisited

TL;DR

This paper investigates four-dimensional quantum gravity using Euclidean dynamical triangulations, mapping phase transitions and analyzing geometric properties to understand the continuum limit and universality of the model.

Contribution

It provides a detailed numerical analysis of the phase structure and geometric dimensions in Euclidean dynamical triangulations, highlighting universality across different models.

Findings

First order phase transitions with decreasing latent heat as fects increase

Hausdorff dimension approaches 4 along the critical line

Spectral dimension is consistent with 1.5 at short distances

Abstract

We conduct numerical simulations of a model of four dimensional quantum gravity in which the path integral over continuum Euclidean metrics is approximated by a sum over combinatorial triangulations. At fixed volume the model contains a discrete Einstein-Hilbert term with coupling $\kappa$ and local measure term with coupling $\beta$ that weights triangulations according to the number of simplices sharing each vertex. We map out the phase diagram in this two dimensional parameter space and compute a variety of observables that yield information on the nature of any continuum limit. Our results are consistent with a line of first order phase transitions with a latent heat that decreases as $\kappa\to\infty$. We find a Hausdorff dimension along the critical line that approaches $D_H=4$ for large $\kappa$ and a spectral dimension that is consistent with $D_s=\frac{3}{2}$ at short distances. These results are broadly in agreement with earlier works on Euclidean dynamical triangulation models which utilize degenerate triangulations and/or different measure terms and indicate that such models exhibit a degree of universality.