Non-Perturbative Gravity and the Spin of the Lattice Graviton

TL;DR

This paper explores the non-perturbative properties of quantum gravity using lattice methods, comparing results with continuum theories to understand the ground state, critical exponents, and the existence of a massless spin-two particle.

Contribution

It provides an explicit lattice ground state wave functional for semiclassical geometries and compares lattice predictions with continuum results near the ultraviolet fixed point.

Findings

Evidence for a massless spin-two particle in the continuum limit.

Lattice and continuum results show similar vacuum-polarization effects.

The derivative of the beta function at the fixed point aligns with continuum predictions.

Abstract

The lattice formulation of quantum gravity provides a natural framework in which non-perturbative properties of the ground state can be studied in detail. In this paper we investigate how the lattice results relate to the continuum semiclassical expansion about smooth manifolds. As an example we give an explicit form for the lattice ground state wave functional for semiclassical geometries. We then do a detailed comparison between the more recent predictions from the lattice regularized theory, and results obtained in the continuum for the non-trivial ultraviolet fixed point of quantum gravity found using weak field and non-perturbative methods. In particular we focus on the derivative of the beta function at the fixed point and the related universal critical exponent $\nu$ for gravitation. Based on recently available lattice and continuum results we assess the evidence for the presence of a massless spin two particle in the continuum limit of the strongly coupled lattice theory. Finally we compare the lattice prediction for the vacuum-polarization induced weak scale dependence of the gravitational coupling with recent calculations in the continuum, finding similar effects.