Lattice quantum gravity with scalar fields

TL;DR

This paper explores a lattice model of four-dimensional quantum gravity coupled with scalar fields, investigating mass renormalization, potential gravitational attraction, and the feasibility of measuring related physical quantities.

Contribution

It introduces a minimally coupled scalar field into the lattice quantum gravity model and discusses methods to measure mass anomalous dimension and gravitational binding energy.

Findings

Scalar field mass undergoes multiplicative renormalization

Potential for measuring gravitational binding energy between scalar particles

Evidence suggests the model exhibits an attractive gravitational force

Abstract

We consider the four-dimensional Euclidean dynamical triangulations lattice model of quantum gravity based on triangulations of $S^{4}$. We couple it minimally to a scalar field in the quenched approximation. Our results suggest a multiplicative renormalization for the mass of the scalar field which is consistent with the shift symmetry of the discretized lattice action. We discuss the possibility of measuring the mass anomalous dimension and the gravitational binding energy between two scalar test particles, where a negative bound state energy would imply that this model has an attractive gravitational force.