pyCICY - v0.5

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

Quickstart

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

Documentation can be found on readthedocs pyCICY.

Literature

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{http://github.com/cbouilla/spasm}}
}

Useful software

pyCICY works nicely with Sage. Other useful packages for dealing with Calabi Yau manifolds in toric varieties are cohomCalg and PALP.