FtheoryTools.jl

Status

This project has been integrated into OSCAR. Future development will therefore happen in the OSCAR repository. More information is available in the latest OSCAR documentation. See here for the documentation of the latest development version. The documentation of the latest stable release is available here.

Goal

The package FTheoryTools.jl aims to automate a number of recuring and (at least in part) tedious computations in F-theory model building. Specifically we focus on the following setups:

• 4d F-theory compactifications,
• defined by a global and singular Weierstrass model as codimension 1 locus of a toric ambient space $Y$,
• which can be crepantly resolved. Some of the techniques/algorithms extend naturally to more general settings. For example, it is not at all necessary to restrict to 4-dimensional settings (or alternatively, base spaces of dimension 3). Indeed, the current implementation does allow for arbitrary base dimension. For more extensions that we might address in the future, please take a look at the section "possibly future extensions" below.

We aim for the following workflow:

• User input:
  • Weierstrass polynomial $P_W$,
  • Data defining the toric ambient space $Y$ (if applicable),
  • Choice of resolved phase (if applicable),
  • Generating sections (for $U(1)$ symmetries).
• Output:
  • Singular loci in codimension 1, 2 and 3.
  • Defining data of resolved geometry.
  • (Pictures of) fibre diagrams of resolved fibre over the originally singular loci, including intersections of $U(1)$-sections.
  • Gauge group.
  • Topological data (e.g. Euler number).

Possible future extensions

Future extensions include, but are not necessarily limited to, the following:

• Specify a $G_4$-flux and work-out the chiral spectra.
• Specify a gauge potential and work out (candidates for) the line bundles whose cohomologies encode the vector-like spectra.
• Other singularity types (non-minimal, terminal, etc.)
• Base blowups for singularity resolution.

Dependencies

We base this project on OSCAR for general functionality on toric spaces and (possibly even more importantly) polynomial operations. The latter are based on Singular and Singular.jl, respectively.

Code coverage and tests

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• .

Installation instructions for Linux

1. Install Julia on your computer. The latest version can be found here.
2. Download this development version of FTheoryTools.jl. Those interested in contributing should instead clone this repository:

    git clone https://github.com/Julia-meets-String-Theory/FTheoryTools.jl.git

3. Place your clone/download in a location outside of the .julia folder of your home folder.
4. Finally, register and build FTheoryTools.jl as follows:

    using Pkg
    Pkg.add("Oscar")
    Pkg.develop(path="path/to/your/FTheoryTools.jl")
    Pkg.build("FTheoryTools")

5. To use your FTheoryTools installation, you finally want to invoke

    using Oscar, FTheoryTools

Note that due to the modularity of the Julia programing language, access to the Oscar functionality is not available in the REPL unless you issue using("Oscar") explicitly. This is the reason for why this command appears in the examples of our documentation.

You can instruct Julia to automatically conduct the above steps upon starting, so that you immediately have access to FTheoryTools (and Oscar). To this end perform the following steps:

1. Navigate to the hidden julia folder in your home directory (e.g. via cd .julia/ in the terminal).
2. In this folder, create (if not already existing) the folder config.
3. In the config folder create (unless existing) the file startup.jl.
4. Add the following lines to the file startup.jl:

using Pkg
using Oscar
Pkg.develop(path="path/to/your/FTheoryTools.jl")
using FTheoryTools

Documentation

For detailed information about the implemented functionality, please take a look at the most recent documentation.

Bugs and feature requests

If you want to report a bug or request a feature, please do it by raising a github issue.

Contributions

Contributions are highly appreciated. Please notice that:

• Contributions must be done by opening a pull request.
• Pull requests must pass a number of checks that are automatically conducted by our test suite, before they can be merged. A further approval by a code owner is appreciated.
• Code is expected to be in agreement with the Oscar style guide.

Contact

This software is work in progress of

• Martin Bies,
• Andrew Turner.

We appreciate insightful discussions with Mirjam Cvetič.

If you are interested in contributing, please feel free to reach out to us for more details.

Citation

If FTheoryTools has been used in your research, please use the bibtex below or download it here:

@Misc{FTheoryTools,
  author       = "Bies, Martin and Turner, Andrew P.",
  howpublished = {\url{https://github.com/Julia-meets-String-Theory/FTheoryTools.jl}},
  title        = {FTheoryTools -- Julia tools for F-Theory compactifications},
  year         = "2022"
}

Funding

The work of Martin Bies is supported by SFB-TRR 195 Symbolic Tools in Mathematics and their Application of the German Research Foundation (DFG).

The work of Andrew Turner is supported by DOE (HEP) Award DE-SC001352.