Non-Local Symmetries of Planar Feynman Integrals

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.

8 pages, v2: minor edits

References in corpus (8)

• The SAGEX Review on Scattering Amplitudes
• Lectures on Yangian Symmetry
• Yangian-invariant fishnet integrals in 2 dimensions as volumes of Calabi-Yau varieties
• Traintrack Calabi-Yaus from Twistor Geometry
• Cutting the traintracks: Cauchy, Schubert and Calabi-Yau
• The Loom for General Fishnet CFTs
• Checkerboard CFT
• The Feyn-Structure of Yangian Symmetry

Cited by in corpus (2)

• Boundary bound states and integrable Wilson loops in ABJM
• Hypergeometry from $\hat{\mathrm{P}}$-Symmetry: Feynman Integrals in One and Two Dimensions