heteroticyukawas

fheteroticyukawas is a package designed to calculate the Yukawa couplings/quark masses of general line bundles on the tetraquadric. Necessary inputs are the complex and K\"ahler moduli, line bundle indices, and closed representatives of the 1-form bundle cohomology.

Given that, it calculates, using NN models in TensorFlow, Calabi-Yau metrics, bundle metrics and harmonic representatives of the cohomology. It is based off cymetric, a Python package for learning of moduli-dependent Calabi-Yau metrics using neural networks implemented in TensorFlow.

A calculation can be replicated by navigating to heteroticyukawas/heteroticyukawas setting the moduli in generate_and_train_all_nnsHOLO.py, setting the settings in Model_13_Do.py, and then simply running:

console source ~/cymetric/bin/activate python Model_13_Do.py 0.0000 'phi'

This calculates the matter fields Yukawa couplings for the second model in the paper, for the stabilised value of the K\"ahler moduli, and for complex structure modulus $\psi=0$.

Example output of calculation

Installation

This guide assumes that you have a working Python 3 (preferably python 3.7 or above) installation (and Sage and Mathematica, if you want to use these features as well). So running python3 should work on your system. Moreover, it assumes that you have installed git. Note that both are standard on Mac and most Linux distributions. For Windows, you will typically have to install them and make sure that for example Python works correctly with Mathematica if you are planing on using the Mathematica interface.

1. Install it with Python

If you want to use any existing python installation (note that we recommend using a virtual environment, see below), just run in a terminal console pip install git+https://github.com/kitft/heteroticyukawas.git

To run the example notebooks, you need jupyter. You can install it with console pip install jupyter notebook

2. Install with virtual environment

Using standard virtual environment

Create a new virtual environment in a terminal with

console python3 -m venv ~/cymetric

Then install with pip directly from github

console source ~/cymetric/bin/activate pip install --upgrade pip pip install git+https://github.com/kitft/heteroticyukawas.git pip install jupyter notebook python -m ipykernel install --user --name=cymetric

Using anaconda

Create a new environment with

console conda create -n cymetric python=3.9

Then install with pip directly from github

console conda activate cymetric pip install git+https://github.com/pythoncymetric/cymetric.git

Conventions and normalizations

We summarize the mathematical conventions we use in this .pdf file.

Contributing

We welcome contributions to the project. Those can be bug reports or new features, that you have or want to be implemented. Please read more here.

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