Yangian Symmetry for Fishnet Feynman Graphs

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, $\ensuremath{\gamma}$-twisted $\mathcal{N}=4$ super Yang--Mills or Aharony-Bergman-Jafferis-Maldacena (ABJM) theory. Consequently, the study of fishnet graphs allows us to get deep insights into the integrability of the planar $\mathrm{AdS}/\mathrm{CFT}$ correspondence.