On the Regge limit of Fishnet correlators

TL;DR

This paper investigates the Regge trajectories of Mellin amplitudes in Fishnet theory, revealing exact results for some correlators and perturbative approaches for others, enhancing understanding of this integrable conformal model.

Contribution

It provides the first analysis of Regge trajectories in Fishnet correlators, combining exact and perturbative methods across different magnon sectors.

Findings

Exact Regge poles for 0- and 1-magnon correlators as a function of coupling.

Perturbative evaluation of 2-magnon Mellin amplitudes at weak coupling.

Order of magnitude estimates for strong coupling regime.

Abstract

We study the Regge trajectories of the Mellin amplitudes of the $0-,1-$ and $2-$ magnon correlators of the Fishnet theory. Since fishnet theory is both integrable and conformal, the correlation functions are known exactly. We find that while for $0$ and $1$ magnon correlators, the Regge poles can be exactly determined as a function of coupling, $2$-magnon correlators can only be dealt with perturbatively. We evaluate the resulting Mellin amplitudes at weak coupling, while for strong coupling we do an order of magnitude calculation.