The SAGEX review on scattering amplitudes Chapter 9: Integrability of amplitudes in fishnet theories

We discuss the properties of scattering amplitudes in a conformal bi-scalar fishnet theory that previously appeared in the study of integrable deformations of N = 4 SYM. In distinction with the latter theory, the scattering amplitudes in the conformal fishnet theory do not suffer from infrared divergences and possess enhanced symmetries. We demonstrate that for the simplest four-particle scattering the single-and double-trace partial amplitudes can be computed for arbitrary coupling in the leading color approximation. We also review the invariance of single-trace components of multi-particle fishnet amplitudes in the planar limit under infinite-dimensional Yangian symmetry.