Clear Evidence of a Continuum Theory of 4D Euclidean Simplicial Quantum Gravity

TL;DR

This study uses Monte-Carlo simulations to explore 4D simplicial quantum gravity coupled with matter fields, providing evidence supporting a continuum theory related to conformal gravity in four dimensions.

Contribution

It offers the first numerical evidence linking 4D simplicial quantum gravity to a continuum conformal gravity theory, including matter field effects.

Findings

The string susceptibility exponent gamma^{(4)} depends on matter content.

Numerical results support a relation between 4D simplicial quantum gravity and conformal gravity.

A detailed phase structure with matter fields is proposed.

Abstract

Four-dimensional (4D) simplicial quantum gravity coupled to both scalar fields (N_X) and gauge fields (N_A) has been studied using Monte-Carlo simulations. The matter dependence of the string susceptibility exponent gamma^{(4)} is estimated. Furthermore, we compare our numerical results with Background-Metric-Independent (BMI) formulation conjectured to describe the quantum field theory of gravity in 4D. The numerical results suggest that the 4D simplicial quantum gravity is related to the conformal gravity in 4D. Therefore, we propose a phase structure in detail with adding both scalar and gauge fields and discuss the possibility and the property of a continuum theory of 4D Euclidean simplicial quantum gravity.