Quantum Gravity on the Lattice

TL;DR

This review explores the lattice approach to quantum gravity, its connection to the non-trivial ultraviolet fixed point scenario, and potential observational implications, emphasizing non-perturbative methods and the scale dependence of Newton's constant.

Contribution

It provides a comprehensive overview of lattice quantum gravity methods and their relation to continuum renormalization group results, highlighting the non-perturbative strong gravity regime and observational consequences.

Findings

Lattice results support the non-trivial ultraviolet fixed point scenario.

A scale-dependent Newton's constant may explain the observed cosmological constant.

Connections between infrared gauge theories and quantum gravity are emphasized.

Abstract

I review the lattice approach to quantum gravity, and how it relates to the non-trivial ultraviolet fixed point scenario of the continuum theory. After a brief introduction covering the general problem of ultraviolet divergences in gravity and other non-renormalizable theories, I cover the general methods and goals of the lattice approach. An underlying theme is the attempt at establishing connections between the continuum renormalization group results, which are mainly based on diagrammatic perturbation theory, and the recent lattice results, which apply to the strong gravity regime and are inherently non-perturbative. A second theme in this review is the ever-present natural correspondence between infrared methods of strongly coupled non-abelian gauge theories on the one hand, and the low energy approach to quantum gravity based on the renormalization group and universality of critical behavior on the other. Towards the end of the review I discuss possible observational consequences of path integral quantum gravity, as derived from the non-trivial ultraviolet fixed point scenario. I argue that the theoretical framework naturally leads to considering a weakly scale-dependent Newton's costant, with a scaling violation parameter related to the observed scaled cosmological constant (and not, as naively expected, to the Planck length).