Newtonian binding from lattice quantum gravity

We study scalar fields propagating on Euclidean dynamical triangulations (EDTs). 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 nonrelativistic limit. We find a binding energy compatible with what one expects for the ground state energy by solving the Schrodinger equation for Newton's potential. Agreement with this expectation is obtained in the infinite-volume, continuum limit of the lattice calculation, providing nontrivial 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.

Automated summary

This study investigates scalar fields propagating on Euclidean dynamical triangulations, specifically focusing on the interaction of two scalar particles and the calculation of binding energy for two-particle bound states in the nonrelativistic limit. The results show compatibility of the binding energy with Newton's gravitational potential, suggesting that EDT is a theory of gravity in four dimensions. Additionally, the determination of lattice spacing within an EDT calculation and the ability to reach a continuum limit support the asymptotic safety scenario for gravity.