The SAGEX Review on Scattering Amplitudes, Chapter 9: Integrability of Amplitudes in Fishnet Theories

Understand

We discuss the properties of scattering amplitudes in a conformal bi-scalar fishnet theory that previously appeared in the study of integrable deformations of $\mathcal N=4$ 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 leading color limit under infinite-dimensional Yangian symmetry.