CYMYC

cymyc is a library for numerical differential geometry on Calabi-Yau manifolds written in JAX, enabling performant:

• Approximations of useful tensor fields;
• Computations of curvature-related quantities;
• Investigations of the complex structure moduli space;

in addition to many other features.

Installation

First, clone the project:

git clone git@github.com:Justin-Tan/cymyc.git
cd cymyc

Next, with a working Python installation, create a new virtual environment and run an editable install, which permits local development.

pip install --upgrade pip
python -m venv /path/to/venv
source /path/to/venv/bin/activate

python -m pip install -e .

Requires Python >=3.10 - all needed dependencies will be automatically installed.

Documentation / examples

Check out the docs at justin-tan.github.io/cymyc/. If you are new to Jax and want to get your hands dirty, then start with this example. Also see the example workflow for canonical usage of the scripts in this library.

Contributing / Development

This library is under active development, and the current state is but the leading order approximation. Please open an issue / pull request if you encounter unexpected behaviour. Additionally, feel free to get in touch anytime to discuss the project and help us guide development.

Citation

If you found this library to be useful in academic work, then please cite: (arxiv).

@article{cymyc,
	author = {Butbaia, Giorgi, Tan, Justin, ...},
	title = {\textsf{cymyc}: {\it A \textsf{{JAX}} package for {C}alabi--{Y}au 
	{M}etrics {Y}ukawas and {C}urvature}},
    eprint = "2410.19728",
    archivePrefix = "arXiv",
    primaryClass = "hep-th",
    month = "10",
    year = "2024"
}

Related work

This codebase was used to generate the 'experimental' results for the following publications:

1. Curvature on Calabi-Yau manifolds - arxiv:2211.90801.
2. Physical Yukawa couplings in heterotic string compactifications - arxiv:2401.15078.
3. Precision string phenomenology - arxiv:2407.13836.

Related libraries / Acknowledgements

We would like to acknowledge the authors of the cymetric library (Larfors et. al. (2022)).

Numerical metrics on Calabi-Yaus

• cymetric - Python library for studying Calabi-Yau metrics.
• cyjax - Donaldson's algorithm for Calabi-Yau metrics in Jax.
• MLGeometry - Machine learning Calabi-Yau metrics.

JAX ecosystem

• equinox - JAX enhancement suite.
• flax - Neural network library.