Newtonian Binding from Lattice Quantum Gravity

TL;DR

This paper demonstrates that lattice quantum gravity via Euclidean dynamical triangulations reproduces Newtonian gravity in the appropriate limit, providing evidence for its validity as a four-dimensional theory of gravity and supporting the asymptotic safety scenario.

Contribution

It shows that EDT can recover Newtonian gravitational interactions and determines the lattice spacing, supporting the continuum limit and asymptotic safety in quantum gravity.

Findings

Binding energy matches Schrödinger equation for Newton's potential

Lattice spacings are smaller than the Planck length

Supports EDT as a viable theory of 4D quantum gravity

Abstract

We study scalar fields propagating on Euclidean dynamical triangulations (EDT). In this work we study the interaction of two scalar particles, and we show that in the appropriate limit we recover an interaction compatible with Newton's gravitational potential in four dimensions. Working in the quenched approximation, we calculate the binding energy of a two-particle bound state, and we study its dependence on the constituent particle mass in the non-relativistic limit. We find a binding energy compatible with what one expects for the ground state energy by solving the Schr\"{o}dinger equation for Newton's potential. Agreement with this expectation is obtained in the infinite-volume, continuum limit of the lattice calculation, providing non-trivial evidence that EDT is in fact a theory of gravity in four dimensions. Furthermore, this result allows us to determine the lattice spacing within an EDT calculation for the first time, and we find that the various lattice spacings are smaller than the Planck length, suggesting that we can achieve a separation of scales and that there is no obstacle to taking a continuum limit. This lends further support to the asymptotic safety scenario for gravity.