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 κ and a local measure term with coupling β 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 κ→∞. We find a Hausdorff dimension along the critical line that approaches DH=4 for large κ and a spectral dimension consistent with Ds=32 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.
ASJC Scopus subject areas
- Nuclear and High Energy Physics