Indications for Criticality at Zero Curvature in a 4d Regge Model of Euclidean Quantum Gravity

TL;DR

This paper investigates the phase structure of a 4d Euclidean quantum gravity model using Regge calculus, identifying a critical line at zero curvature with a potential phase transition and crossover behavior.

Contribution

It introduces a cut-off on link lengths, allowing independent control of gravitational coupling and cosmological constant, and maps the zero curvature line in the coupling plane.

Findings

Identifies a zero curvature line in the coupling constant plane.

Finds evidence of a first order phase transition crossing this line.

Suggests a crossover beyond a potential second order endpoint.

Abstract

We re-examine the approach to four-dimensional Euclidean quantum gravity based on the Regge calculus. A cut-off on the link lengths is introduced and consequently the gravitational coupling and the cosmological constant become independent parameters. We determine the zero curvature, $<R> =0$, line in the coupling constant plane by numerical simulations. When crossing this line we find a strong, probably first order, phase transition line with indications of a second order endpoint. Beyond the endpoint the transition through the $<R> =0$ line appears to be a crossover. Previous investigations, using the Regge or the Dynamical Triangulation approach, dealt with a limit in which the first order transition prevails.