# Exact scattering amplitudes in conformal fishnet theory

## TL;DR

This paper calculates exact four-particle scattering amplitudes in conformal fishnet theory, revealing protected and nontrivial components, and derives new representations to analyze high-energy behavior and Regge trajectories.

## Contribution

It provides the first exact expressions for scattering amplitudes in conformal fishnet theory, including a new representation for four-point functions valid at any coupling.

## Key findings

- Single-trace amplitude is quantum correction protected.
- Double-trace amplitude is finite and depends on Mandelstam ratios.
- Results agree with five-loop calculations at weak coupling.

## Abstract

We compute the leading-color contribution to four-particle scattering amplitude in four-dimensional conformal fishnet theory that arises as a special limit of $\gamma$-deformed $\mathcal N=4$ SYM. We show that the single-trace partial amplitude is protected from quantum corrections whereas the double-trace partial amplitude is a nontrivial infrared finite function of the ratio of Mandelstam invariants. Applying the Lehmann--Symanzik--Zimmerman reduction procedure to the known expression of a four-point correlation function in the fishnet theory, we derive a new representation for this function that is valid for arbitrary coupling. We use this representation to find the asymptotic behavior of the double-trace amplitude in the high-energy limit and to compute the corresponding exact Regge trajectories. We verify that at weak coupling the expressions obtained are in agreement with an explicit five-loop calculation.