Yangian-invariant conformal Feynman integrals satisfy a general cross-ratio PDE system that for a class of graphs is exactly a GKZ hypergeometric system.
Basso-Dixon Correlators in Two-Dimensional Fishnet CFT
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abstract
We compute explicitly the two-dimensional version of Basso-Dixon type integrals for the planar four-point correlation functions given by conformal fishnet Feynman graphs. These diagrams are represented by a fragment of a regular square lattice of power-like propagators, arising in the recently proposed integrable bi-scalar fishnet CFT. The formula is derived from first principles, using the formalism of separated variables in integrable SL(2,C) spin chain. It is generalized to anisotropic fishnet, with different powers for propagators in two directions of the lattice.
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Yangian symmetry, GKZ equations and integrable Feynman graphs in conformal variables
Yangian-invariant conformal Feynman integrals satisfy a general cross-ratio PDE system that for a class of graphs is exactly a GKZ hypergeometric system.