CDT Quantum Toroidal Spacetimes: An Overview

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.

Automated summary

Lattice formulations of gravity, such as CDT, are used to study non-perturbative aspects of quantum gravity. The higher-order phase transitions observed in CDT can define a continuum limit of the lattice theory, and studying the model with a toroidal spatial topology can provide insights into the nature of typical quantum fluctuations of geometry. Additionally, including massless scalar fields in the path integral of CDT can have a significant impact on the geometry.