Abstract
We show that all Feynman integrals in two Euclidean dimensions with massless propagators and arbitrary non-integer propagator powers can be expressed in terms of single-valued analogues of Aomoto-Gelfand hypergeometric functions. The latter can themselves be written as bilinears of hypergeometric functions, with coefficients that are intersection numbers in a twisted homology group. As an application, we show that all one-loop integrals in two dimensions with massless propagators can be written in terms of Lauricella \( {F}_D^{(r)} \) functions, while the L-loop ladder integrals are related to the generalised hypergeometric L+1FL functions.
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Acknowledgments
We thank Florian Loebbert, Albrecht Klemm and Christoph Nega for discussions and collaboration on a related project. FP thanks Andrzej Pokraka, Carlos Rodriguez, Oliver Schlotterer and Cathrin Semper for discussions and Robin Marzzucca for collaboration on a related project. This work was co-funded by the European Union (ERC Consolidator Grant LoCoMotive 101043686). Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Research Council. Neither the European Union nor the granting authority can be held responsible for them.
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Duhr, C., Porkert, F. Feynman integrals in two dimensions and single-valued hypergeometric functions. J. High Energ. Phys. 2024, 179 (2024). https://doi.org/10.1007/JHEP02(2024)179
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DOI: https://doi.org/10.1007/JHEP02(2024)179