Euclidean dynamical triangulations revisited

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 lc and a local measure term with coupling /3 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 firstorder phase transitions with a latent heat that decreases as lc -> infinity. We find a Hausdorff dimension along the critical line that approaches DH = 4 for large lc 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.

Automated summary

We numerically simulate a four-dimensional quantum gravity model using combinatorial triangulations to approximate the path integral over continuous Euclidean metrics. By mapping out the phase diagram in a two-dimensional parameter space, we find a line of first-order phase transitions with decreasing latent heat as the coupling lc tends to infinity. The critical line exhibits a Hausdorff dimension approaching DH = 4 for large lc and a spectral dimension consistent with Ds = 32 at short distances. These results suggest a degree of universality in models utilizing degenerate triangulations and/or different measure terms.