Causal Dynamical Triangulations in 1+1D and 2+1D

This repository contains code and documentation for simulating and studying causal dynamical triangulations (CDT) in both 1+1D and 2+1D spacetime dimensions.

Introduction

Causal Dynamical Triangulations is an approach to quantum gravity, where spacetime is approximated by a simplicial complex. The dynamics of spacetime is described through the evolution of this complex, which is constructed by gluing together simple building blocks known as simplices. In (1+1)D and (2+1)D, these simplices are triangles and tetrahedra respectively.

Repository Structure

CDT/
├── src/
│   │
│   ├── 1+1/
│   │   │
│   │   ├── classes/
│   │   │   ├── __init__.py
│   │   │   ├── bag.py
│   │   │   ├── pool.py
│   │   │   ├── simulation.py
│   │   │   ├── triangle.py
│   │   │   ├── universe.py
│   │   │   └── vertex.py
│   │   │
│   │   └── main.py
│   │
│   ├── 2+1/
│   │   │
│   │   ├── classes/
│   │   │   │
│   │   │   ├── helper_functions/
│   │   │   │   ├── __init__.py
│   │   │   │   ├── generate_initial.py
│   │   │   │   └── helpers.py
│   │   │   │
│   │   │   ├── initial_universes/
│   │   │   │   └── initial_t3.CDT
│   │   │   │
│   │   │   ├── __init__.py
│   │   │   ├── bag.py
│   │   │   ├── check_mt.py
│   │   │   ├── observable.py
│   │   │   ├── pool.py
│   │   │   ├── simulation.py
│   │   │   ├── simulation_mt.py
│   │   │   ├── tetra.py
│   │   │   ├── universe.py
│   │   │   ├── universe_mt.py
│   │   │   └── vertex.py
│   │   │
│   │   ├── __init__.py
│   │   └── main.py
│   │
│   └── __init__.py
│
├── .gitignore
├── README.md
├── requirements.txt
└── __init__.py

Usage

To use the code in this repository, follow the steps below:

1. Install the dependencies: Ensure you have Python installed. Then install the required Python packages using pip:

   pip install -r requirements.txt

2. Running simulations:

   • For (1+1)D simulations, navigate to the src/1+1/ directory and run the main script:

     cd src/1+1/
     python main.py

   • For (2+1)D simulations, navigate to the src/2+1/ directory and run the main script:

     cd src/2+1/
     python main.py

3. Configuration:

   • You can configure the simulation parameters by editing the configuration files or passing parameters directly to the simulation scripts.

Acknowledgements

Reference paper and codebase:

• Simulating CDT quantum gravity (Brunekreef, Loll, and Görlich, 2024)

References

For more information about Causal Dynamical Triangulations, refer to the following resources:

• Quantum Gravity from Causal Dynamical Triangulations: A Review (Loll, 2019)
• Causal Dynamical Triangulations Wikipedia
• CDT Research Papers

License

This project is licensed under the MIT License. See the LICENSE file for more details.