Nonlocal Symmetries of Planar Feynman Integrals
Florian Loebbert1, Lucas Rüenaufer1, Sven F Stawinski1
1Universität Bonn, Bethe Center for Theoretical Physics, D-53115 Bonn, Germany.
Physical Review Letters
|October 25, 2025
Summary
Scalar Feynman graphs exhibit Yangian level-one momentum symmetry under specific propagator power constraints. This invariance, linked to conformal structures, extends to full Yangian symmetry for various Feynman integrals.
Area of Science:
- Quantum Field Theory
- Mathematical Physics
Background:
- Scalar Feynman graphs are crucial in quantum field theory.
- Yangian symmetry has been observed in specific examples like fishnet graphs.
- Conformal symmetries in position space have been studied.
Purpose of the Study:
- To prove the invariance of scalar Feynman graphs under Yangian level-one momentum symmetry.
- To establish a connection between momentum-space and position-space symmetries.
- To generalize Yangian symmetry to a broader class of Feynman integrals.
Main Methods:
- Relating Yangian symmetry to planarized conformal simplices.
- Proving momentum-space analogue of position-space conformal conditions.
- Analyzing propagator power constraints.
Main Results:
- Invariance of scalar Feynman graphs of any planar topology under Yangian level-one momentum symmetry is proven.
- A momentum-space conformal condition on propagator powers is established.
- Full Yangian symmetry is implied for graphs satisfying both conditions.
Conclusions:
- The study provides a general proof for Yangian symmetry in scalar Feynman integrals.
- This work unifies previous examples and extends to massive propagators.
- The findings bridge concepts from conformal field theory and scattering amplitudes.
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