Dynamical Triangulations, a Gateway to Quantum Gravity ?

TL;DR

This paper demonstrates how dynamical triangulations can be used to formulate two-dimensional quantum gravity as a scaling limit of statistical systems, providing insights into higher-dimensional quantum gravity and potential non-perturbative formulations.

Contribution

It introduces a discretized approach to quantum gravity via dynamical triangulations, linking geometric scaling relations to critical phenomena and exploring higher-dimensional extensions.

Findings

Scaling relations with simple geometric interpretations

Calculation of Hartle-Hawking wave functionals and geodesic correlation functions

Numerical evidence of a fixed point in four-dimensional quantum gravity

Abstract

We show how it is possible to formulate Euclidean two-dimensional quantum gravity as the scaling limit of an ordinary statistical system by means of dynamical triangulations, which can be viewed as a discretization in the space of equivalence classes of metrics. Scaling relations exist and the critical exponents have simple geometric interpretations. Hartle-Hawkings wave functionals as well as reparametrization invariant correlation functions which depend on the geodesic distance can be calculated. The discretized approach makes sense even in higher dimensional space-time. Although analytic solutions are still missing in the higher dimensional case, numerical studies reveal an interesting structure and allow the identification of a fixed point where we can hope to define a genuine non-perturbative theory of four-dimensional quantum gravity.