Quantum Gravity from Simplices: Analytical Investigations of Causal Dynamical Triangulations

TL;DR

This paper explores analytical methods in Causal Dynamical Triangulations, a promising approach to quantum gravity, by studying low-dimensional models and their continuum limits to deepen understanding beyond numerical simulations.

Contribution

It advances analytical understanding of CDT models in low dimensions, including coupled matter systems and specific solvable models, complementing numerical results.

Findings

Analytical solutions for (1+1)-dimensional CDT with Ising matter.

Continuum limit of a (2+1)-dimensional CDT model.

Enhanced theoretical insights into quantum gravity models.

Abstract

A potentially powerful approach to quantum gravity has been developed over the last few years under the name of Causal Dynamical Triangulations. Numerical simulations have given very interesting results in the cases of two, three and four spacetime dimension. The aim of this thesis is to give an introduction to the subject (Chapter 1), and try to push the analytical understanding of these models further. This is done by first studying (Chapter 2) the case of a (1+1)-dimensional spacetime coupled to matter, in the form of an Ising model, by means of high- and low-temperature expansions. And after (Chapter 3) by studying a specific model in (2+1) dimensions, whose solution and continuum limit are presented.