CDT Quantum Toroidal Spacetimes: An Overview
arXiv:2103.15610
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.
arXiv comment36 pages, a lot of figures
References in corpus (17)
- Quantum Gravity at a Lifshitz Point
- Emergence of a 4D World from Causal Quantum Gravity
- Reconstructing the Universe
- General Covariance in Quantum Gravity at a Lifshitz Point
- The Nonperturbative Quantum de Sitter Universe
- Focusing on the Fixed Point of 4D Simplicial Gravity
- Critical Behavior of Dynamically Triangulated Quantum Gravity in Four Dimensions
- Baby universes in 2d quantum gravity
- A String Field Theory based on Causal Dynamical Triangulations
- Quantum Gravity, Dynamical Triangulation and Higer Derivative Regularization
- Exploring Euclidean Dynamical Triangulations with a Non-trivial Measure Term
- Impact of topology in causal dynamical triangulations quantum gravity
- Stochastic quantization and the role of time in quantum gravity
- The phase structure of Causal Dynamical Triangulations with toroidal spatial topology
- Four-dimensional CDT with toroidal topology
- Pseudo-Cartesian coordinates in a model of Causal Dynamical Triangulations
- Properties of dynamical fractal geometries in the model of Causal Dynamical Triangulations