Euclidean Dynamical Triangulations Revisited

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.