Non-Local Symmetries of Planar Feynman Integrals

TL;DR

This paper proves that scalar planar Feynman integrals exhibit Yangian symmetry under certain conditions, extending known symmetries from specific examples to a broader class of integrals including massive cases.

Contribution

It establishes a general proof of Yangian invariance for planar scalar Feynman graphs with constraints on propagator powers, linking conformal simplices to momentum-space symmetry.

Findings

Yangian symmetry holds for all scalar planar Feynman integrals under specified conditions.

The proof connects conformal simplices to momentum-space invariance.

Includes integrals with massive propagators, broadening previous results.

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.