Continuum interpretation of the dynamical-triangulation formulation of quantum Einstein gravity

TL;DR

This paper interprets the phases of non-perturbative quantum Einstein gravity via continuum spacetimes with positive or negative curvature, linking numerical simulation results to geometric properties and phase transition behavior.

Contribution

It provides a continuum interpretation of the crumpled and elongated phases in dynamical triangulation quantum gravity, connecting numerical results to geometric curvature concepts.

Findings

Crumpled phase associated with negative curvature and a large mother universe.

Elongated phase characterized by positive curvature and branched-polymer structure.

Evidence of scaling behavior in the crumpled phase.

Abstract

In the time-space symmetric version of dynamical triangulation, a non-perturbative version of quantum Einstein gravity, numerical simulations without matter have shown two phases, with spacetimes that are either crumpled or elongated like branched polymers, with strong evidence of a first-order transition between them. These properties have generally been considered unphysical. Using previously unpublished numerical results, we give an interpretation in terms of continuum spacetimes that have constant positive and negative curvature, respectively in the 'elongated' and 'crumpled' phase. The magnitude of the positive curvature leads naturally to average spacetimes consisting solely of baby-universes in a branched-polymer structure, whereas the negative curvature accommodates easily a large mother universe, albeit with a crumpling singularity. Nevertheless, there is evidence for scaling in the crumpled phase, which we compare with the well-known scaling in the elongated phase. Using constraint effective-action models we analyze existing numerical susceptibility-data of the phase transition and determine the behavior of the average Regge-curvature. We propose a renormalization of the Regge curvature and compare it to the curvature of the above continuum spacetimes, and also to the curvature implied by the Gauss-Bonnet theorem in the continuum. The latter involves a more benign multiplicative renormalization and suggests that simulations at larger volumes are needed to settle the order of the phase transition.