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

TL;DR

This paper explores the integrability and symmetry properties of scattering amplitudes in a conformal fishnet theory, highlighting their divergence-free nature and invariance under Yangian symmetry, with explicit computations for four-particle scattering.

Contribution

It demonstrates that scattering amplitudes in the conformal fishnet theory are divergence-free, possess enhanced symmetries, and can be computed explicitly for arbitrary coupling in the leading color limit.

Findings

Scattering amplitudes are free from infrared divergences.

Single- and double-trace amplitudes can be computed explicitly.

Amplitudes exhibit invariance under Yangian symmetry.

Abstract

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.