pyCICY

Calabi-Yau manifolds are an important ingredient in string theory compactifications. Their topological quantities can be related to, for example, the number of massless fermion generations in the four-dimensional theory. Complete Intersection Calabi-Yau (CICY) manifolds are one of the most common constructions. There are 7890 three-folds and almost a million four-folds.

The package

pyCICY lets you compute various quantites, such as Chern classes, triple intersection numbers or Hodge numbers of tangent and line bundles. It’s a python package mostly utilizing numpy for the underlying computations. Installation is straightforwad with pip. For the latest version install from github

pip install --user git+https://github.com/robin-schneider/CICY

The Quintic

Take for example the quintic manifold given by a homogeneous polynomial of degree five in \(\mathbb{P}^4\):

We import the CICY module

from pyCICY import CICY
import numpy as np

define the configuration matrix as a numpy array and initialize a new CICY object

configuration_matrix = np.array([[4,5]])
quintic = CICY(configuration_matrix)

Next we can compute the Hodge numbers of a line bundle

with

line_bundle = [3]
quintic.line_co(line_bundle)
>>> array([35.,  0.,  0.,  0.])

For a full list of functionality run:

help(M)