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Nonlocal Symmetries of Planar Feynman Integrals

Florian Loebbert*, Lucas Rüenaufer†, and Sven F. Stawinski‡

  • *Contact author: loebbert@uni-bonn.de
  • †Contact author: lucas@rueenaufer.de
  • ‡Contact author: sstawins@uni-bonn.de
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Phys. Rev. Lett. 135, 151603 – Published 10 October, 2025

DOI: https://doi.org/10.1103/fvzk-dp1b

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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Phys. Rev. Lett. 135, 151603– Published 10 October, 2025
  • Received 19 May 2025
  • Revised 27 August 2025
  • Accepted 4 September 2025
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