Two-point functions in 4D dynamical triangulation

TL;DR

This paper investigates two-point functions of scalar curvature in 4D Euclidean quantum gravity using dynamical triangulation, revealing phase-dependent behaviors and a need for specific subtractions to analyze correlations.

Contribution

It introduces a method to measure and analyze two-point functions in 4D dynamical triangulation, highlighting phase-dependent behaviors and a novel subtraction approach.

Findings

Power law behavior in transition and elongated phase

No simple description in crumpled phase

Subtraction of squared one-point function is necessary

Abstract

In the dynamical triangulation model of 4D euclidean quantum gravity we measure two-point functions of the scalar curvature as a function of the geodesic distance. To get the correlations it turns out that we need to subtract a squared one-point function which, although this seems paradoxical, depends on the distance. At the transition and in the elongated phase we observe a power law behaviour, while in the crumpled phase we cannot find a simple function to describe it.