Field-theory limit of half-maximal string loop amplitudes

This repository contains Wolfram Mathematica notebooks and source code supporting the results presented in:

Marcus Berg, Michael Haack and Yonatan Zimmerman,
One-loop Amplitudes: String Methods, Infrared Regularization, and Automation, 2026. https://arxiv.org/abs/2603.26892

The notebooks reproduce key calculations from the paper and provide an explicit implementation of the methods described therein.

Contents

• Field Theory Integral Calculations: Mathematica notebooks reproducing calculations form section 6 in the paper.
• Building Blocks.m : Repository saving key calculationd from the above file to be used in `Assembly and Results'.
• Assembly and Results: Mathematica notebooks reproducing calculations from section 7 in the paper.
• Berends Giele BCJ Identities: Mathematica notebooks corroborating identities form appendix A.4 in the paper.
• Half-Maximal Four-Point One-Loop Amplitudes: Mathematica notebooks reproducing calculations form:

  M. Berg, I. Buchberger and O. Schlotterer From maximal to minimal supersymmetry in string loop amplitudes JHEP 04 (2017) 163, [1603.05262].

Requirements

• Wolfram Mathematica (tested with version 14.2)

Usage

This repository is intended to be run locally, not on GitHub itself.
Clone or download the repository, open the desired notebook in Wolfram Mathematica, and evaluate the cells you are interested in.
Some notebooks rely on shared code (e.g. Building Blocks.m), so the relative folder structure should be preserved.

Citation

If you use this code, please cite the accompanying paper and this repository. See CITATION. If you use this code, please cite:

Marcus Berg, Michael Haack and Yonatan Zimmerman,
One-loop Amplitudes: String Methods, Infrared Regularization, and Automation, 2026.
https://arxiv.org/abs/2603.26892

BibTeX:

@article{Berg:2026ufz,
    author = "Berg, Marcus and Haack, Michael and Zimmerman, Yonatan",
    title = "{One-loop Amplitudes: String Methods, Infrared Regularization, and Automation}",
    eprint = "2603.26892",
    archivePrefix = "arXiv",
    primaryClass = "hep-th",
    month = "3",
    year = "2026"
}

License

See LICENSE.