Yangians, Fishnets, and GKZ Systems

The subject of my talk lies at the intersection of two rapidly evolving areas of theoretical physics: integrability in quantum field theory and the computation of Feynman integrals. One of the key players here is fishnet theory—a recently formulated quantum field theory with numerous remarkable properties, yet significantly simpler than more typical examples, such as supersymmetric Yang-Mills theory.
I will discuss the multi-loop Feynman diagrams of this theory, which take the form of a fishnet and exhibit extended symmetries, potentially enabling their complete computation. These symmetries manifest as differential equations, making this discussion part of a larger project focused on the study of the differential equation method for computing multi-loop Feynman diagrams.
I will demonstrate that these equations can be reduced to the well-known Gelfand-Kapranov-Zelevinsky (GKZ) equations in mathematics and outline further prospects.