Archiving this repository as I won't be working on this anymore after having finished my PhD research.
A python CICY toolkit, which allows the computation of line bundle cohomologies over Complete Intersection Calabi Yau manifolds. It further contains functions for determining various topological quantities, such as Chern classes, triple intersection and Hodge numbers.
Installation is straighforwad with pip
pip install pyCICY
or get the latest version
pip install --upgrade git+https://github.com/robin-schneider/CICY.git
We import the CICY object from the module
from pyCICY import CICY
Next we define a CICY, for example the tetraquadric:
M = CICY([[1,2],[1,2],[1,2],[1,2]])
Now we are able to do some calculations, e.g.
M.line_co([1,2,-4,1])
determines the hodge numbers of the line bundle L = O(1,2,-4,1).
Since the rank computation takes the most time we included SpasM - github. The rank_hybrid executable of SpaSM has to be in your $PATH.
T = CICY([[1,2,0,0,0],[1,0,2,0,0],[1,0,0,2,0],[1,0,0,0,2],[3,1,1,1,1]])
and do some computations:
T.line_co([3,-4,2,3,5], SpaSM=True)
Documentation can be found on readthedocs pyCICY.
The module has been developed in the context of the following paper:
@article{Larfors:2019sie,
author = "Larfors, Magdalena and Schneider, Robin",
title = "{Line bundle cohomologies on CICYs with Picard number two}",
eprint = "1906.00392",
archivePrefix = "arXiv",
primaryClass = "hep-th",
reportNumber = "UUITP-18/19",
doi = "10.1002/prop.201900083",
journal = "Fortsch. Phys.",
volume = "67",
number = "12",
pages = "1900083",
year = "2019"
}
Further literature can be found here:
@book{Hubsch:1992nu,
author = "Hubsch, Tristan",
title = "{Calabi-Yau manifolds: A Bestiary for physicists}",
publisher = "World Scientific",
address = "Singapore",
year = "1994",
ISBN = "9789810219277, 981021927X",
SLACcitation = "%%CITATION = INSPIRE-338506;%%"
}
@phdthesis{Anderson:2008ex,
author = "Anderson, Lara Briana",
title = "{Heterotic and M-theory Compactifications for String
Phenomenology}",
school = "Oxford U.",
url = "https://inspirehep.net/record/793857/files/arXiv:0808.3621.pdf",
year = "2008",
eprint = "0808.3621",
archivePrefix = "arXiv",
primaryClass = "hep-th",
SLACcitation = "%%CITATION = ARXIV:0808.3621;%%"
}
The SpaSM library can be found here: github
@manual{spasm,
title = {{SpaSM}: a Sparse direct Solver Modulo $p$},
author = {The SpaSM group},
edition = {v1.2},
year = {2017},
note = {\url{https://github.com/cbouilla/spasm}}
}
pyCICY works nicely with Sage. Other useful packages for dealing with Calabi Yau manifolds in toric varieties are cohomCalg and PALP.