Newtonian Potential in Quantum Regge Gravity

TL;DR

This paper computes the Newtonian potential within a lattice quantum gravity framework, revealing a Yukawa-like potential near the critical point and estimating the effective Newton constant.

Contribution

It introduces a method to calculate the Newtonian potential in simplicial quantum gravity and analyzes its behavior near the critical point in the model.

Findings

The potential becomes Yukawa-like near the critical point.

The mass parameter of the potential decreases as the critical point is approached.

An estimate for the effective Newton constant is provided near the critical point.

Abstract

We show how the Newtonian potential between two heavy masses can be computed in simplicial quantum gravity. On the lattice we compute correlations between Wilson lines associated with the heavy particles and which are closed by the lattice periodicity. We check that the continuum analog of this quantity reproduces the Newtonian potential in the weak field expansion. In the smooth anti-de Sitter-like phase, which is the only phase where a sensible lattice continuum limit can be constructed in this model, we attempt to determine the shape and mass dependence of the attractive potential close to the critical point in $G$. It is found that non-linear graviton interactions give rise to a potential which is Yukawa-like, with a mass parameter that decreases towards the critical point where the average curvature vanishes. In the vicinity of the critical point we give an estimate for the effective Newton constant.