Lattice Quantum Gravity: EDT and CDT

TL;DR

This paper reviews lattice approaches to quantum gravity using EDT and CDT, highlighting their success in 2D and exploring their potential to define a non-perturbative quantum gravity theory in 4D.

Contribution

It provides an overview of EDT and CDT as lattice regularizations for quantum gravity and discusses their role in searching for a non-perturbative UV fixed point in 4D.

Findings

Successful application of EDT and CDT in 2D quantum gravity

Potential of lattice methods to define quantum gravity at sub-Planck scales

Discussion of non-perturbative UV fixed points in 4D

Abstract

This article is an overview of the use of so-called Euclidean Dynamical Triangulations (EDT) and Causal Dynamical Triangulations (CDT) as lattice regularizations of quantum gravity. The lattice regularizations have been very successful in the case of two-dimensional quantum gravity, where the lattice theories indeed provide regularizations of continuum well defined quantum gravity theories. In four-dimensional spacetime the Einstein-Hilbert action leads to a theory of gravity which is not renormalizable as a perturbative quantum theory around flat spacetime. It is discussed how lattice gravity in the form of EDT or CDT can be used to search for a non-perturbative UV fixed point of the lattice renormalization group in the spirit of asymptotic safety. In this way it might be possible to define a quantum theory of gravity also at lengthscales smaller than the Planck length.