Yangian symmetry for fishnet Feynman graphs

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, γ-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.

Gluing Ladder Feynman Diagrams into Fishnets

“…[9][10][11]. In that theory, the gluons and fermions are decoupled, the correlator (1) is a particular instance of the off-shell amplitudes discussed in ref.…”

“…In that theory, the gluons and fermions are decoupled, the correlator (1) is a particular instance of the off-shell amplitudes discussed in ref. [11], and fig. 1 is the only diagram contributing to it.…”

“…It can also assist in the computation of individual Feynman diagrams, in scalar theories directly [7,8], or after suitably twisting the SYM theory [9][10][11], or, more implicitly, through the "hexagonalization" of correlation functions [5].…”

Yangian bootstrap for conformal Feynman integrals

“…Facing these problems, theorists are challenged to identify new methods to evaluate these integrals and to unveil their deeper mathematical structure. Recently a new infinite dimensional Yangian symmetry was identified for a large class of so-called fishnet Feynman graphs [1,2]. In the present paper we explore this connection between Feynman integrals and the theory of integrable models, which play a crucial role for developing analytical methods in all areas of physics.…”

“…Being a member of the class of fishnet Feynman graphs discussed in [1,2], also the double box integral is invariant under the conformal Yangian algebra: (75) In this case conformal symmetry dictates that I 3,3 is of the formÎ…”