Scaling in four dimensional quantum gravity

TL;DR

This paper investigates phase transitions and critical behavior in four-dimensional simplicial quantum gravity using a novel algorithm, revealing a continuous transition between branched polymer and crumpled phases, with implications for non-perturbative quantum gravity.

Contribution

It introduces 'baby universe surgery' to study critical phenomena in 4D quantum gravity and characterizes the phase transition and properties of two distinct phases.

Findings

The phase transition is continuous with accurately measured critical exponents.

Two phases identified: elongated phase with Hausdorff dimension two, crumpled phase with infinite dimension.

The transition point may serve as a non-perturbative quantum gravity candidate.

Abstract

We discuss scaling relations in four dimensional simplicial quantum gravity. Using numerical results obtained with a new algorithm called ``baby universe surgery'' we study the critical region of the theory. The position of the phase transition is given with high accuracy and some critical exponents are measured. Their values prove that the transition is continuous. We discuss the properties of two distinct phases of the theory. For large values of the bare gravitational coupling constant the internal Hausdorff dimension is {\em two} (the elongated phase), and the continuum theory is that of so called branched polymers. For small values of the bare gravitational coupling constant the internal Hausdorff dimension seems to be {\em infinite} (the crumpled phase). We conjecture that this phase corresponds to a theory of topological gravity. {\em At} the transition point the Hausdorff dimension might be finite and larger than two. This transition point is a potential candidate for a non-perturbative theory of quantum gravity.