Grand-Canonical simulation of 4D simplicial quantum gravity

TL;DR

This paper presents a detailed numerical study of 4D simplicial quantum gravity using Grand-Canonical Monte-Carlo simulations, focusing on the conformal mode and string susceptibility, suggesting a connection to continuum 4D quantum gravity.

Contribution

It introduces a comprehensive numerical approach to 4D quantum gravity, emphasizing the conformal mode dependence and calculating the string susceptibility exponent.

Findings

Successful estimation of the string susceptibility exponent.

Evidence that 4D SQG approaches continuum 4D QG.

Insights into the properties of 4D simplicial quantum gravity.

Abstract

A thorough numerical examination for the field theory of 4D quantum gravity (QG) with a special emphasis on the conformal mode dependence has been studied. More clearly than before, we obtain the string susceptibility exponent of the partition function by using the Grand-Canonical Monte-Carlo method. Taking thorough care of the update method, the simulation is made for 4D Euclidean simplicial manifold coupled to $N_X$ scalar fields and $N_A$ U(1) gauge fields. The numerical results suggest that 4D simplicial quantum gravity (SQG) can be reached to the continuum theory of 4D QG. We discuss the significant property of 4D SQG.