Yangian Symmetry for Fishnet Feynman Graphs

TL;DR

This paper demonstrates that certain fishnet Feynman graphs possess Yangian symmetry, leading to new differential equations and providing insights into integrability within the planar AdS/CFT correspondence.

Contribution

It establishes Yangian symmetry for various fishnet Feynman graphs across multiple dimensions, revealing their integrability properties and deriving novel differential equations for complex integrals.

Findings

Yangian symmetry identified in fishnet graphs across 3, 4, and 6 dimensions.

New differential equations derived for fishnet Feynman integrals.

Fishnet graphs in 3 and 4 dimensions dominate specific correlation functions and scattering amplitudes.

Abstract

Various classes of fishnet Feynman graphs are shown to feature a Yangian symmetry over the conformal algebra. We explicitly discuss scalar graphs in three, four and six spacetime dimensions as well as the inclusion of fermions in four dimensions. The Yangian symmetry results in novel differential equations for these families of largely unsolved Feynman integrals. Notably, the considered fishnet graphs in three and four dimensions dominate the correlation functions and scattering amplitudes in specific double scaling limits of planar, gamma-twisted N=4 super Yang-Mills or ABJM theory. Consequently, the study of fishnet graphs allows us to get deep insights into the integrability of the planar AdS/CFT correspondence.