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arXiv · 2505.05550

Non-Local Symmetries of Planar Feynman Integrals

Florian Loebbert·Lucas Rüenaufer·Sven F. Stawinski
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Abstract

We prove the invariance of scalar Feynman graphs of any planar topology under the Yangian level-one momentum symmetry given certain constraints on the propagator powers. The proof relies on relating this symmetry to a planarized version of the conformal simplices of Bzowski, McFadden and Skenderis. In particular, this proves a momentum-space analogue of the position-space conformal condition on propagator powers. When combined with the latter, the invariance under the level-one momentum implies full Yangian symmetry of the considered graphs. These include all scalar Feynman integrals for which a Yangian symmetry was previously demonstrated at the level of examples, e.g. the fishnet or loom graphs, as well as generalizations to graphs with massive propagators.

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Florian Loebbert, Lucas Rüenaufer, Sven F. Stawinski. 2025-05-08. Non-Local Symmetries of Planar Feynman Integrals. https://doi.org/10.1103/fvzk-dp1b

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