CDT Quantum Toroidal Spacetimes: An Overview

TL;DR

This paper reviews the use of Causal Dynamical Triangulations (CDT) in quantum gravity, emphasizing the advantages of toroidal spatial topology for studying phase transitions and quantum fluctuations.

Contribution

It highlights the benefits of toroidal topology in CDT, especially for analyzing phase transitions and the role of scalar fields in quantum geometry.

Findings

Toroidal topology facilitates the study of phase transitions.

Scalar fields influence the fractal structure of quantum geometry.

Topology choice affects the understanding of quantum fluctuations.

Abstract

Lattice formulations of gravity can be used to study non-perturbative aspects of quantum gravity. Causal Dynamical Triangulations (CDT) is a lattice model of gravity that has been used in this way. It has a built-in time foliation but is coordinate-independent in the spatial directions. The higher-order phase transitions observed in the model may be used to define a continuum limit of the lattice theory. Some aspects of the transitions are better studied when the topology of space is toroidal rather than spherical. In addition, a toroidal spatial topology allows us to understand more easily the nature of typical quantum fluctuations of the geometry. In particular, this topology makes it possible to use massless scalar fields that are solutions to Laplace's equation with special boundary conditions as coordinates that capture the fractal structure of the quantum geometry. When such scalar fields are included as dynamical fields in the path integral, they can have a dramatic effect on the geometry.