Regge amplitudes in Generalized Fishnet and Chiral Fishnet Theories

TL;DR

This paper develops a systematic perturbative approach to analyze Regge trajectories of Mellin amplitudes in generalized and chiral Fishnet theories across various dimensions, confirming results with exact methods and extending previous work.

Contribution

It introduces a generic perturbative method for studying Regge trajectories in Fishnet theories applicable in arbitrary dimensions, including new results for 8-dimensional cases.

Findings

Perturbative Regge trajectories match known 4D results.

Results for 8D correlators agree with exact techniques.

Closed-form expressions obtained for chiral Fishnet correlator with two couplings.

Abstract

We extend the analysis of \cite{Chowdhury:2019hns} to study the Regge trajectories of the Mellin amplitudes of the $0-$ and $1-$ magnon correlators of the generalized Fishnet theory in $d$ dimensions and one type of correlators of chiral fishnet theory in $4$ dimensions. We develop a systematic procedure to perturbatively study the Regge trajectories and subsequently perform the spectral integral. Our perturbative method is very generic and in principle can be applied to correlators whose perturbative Regge trajectories obey some structural conditions which we list down. Our $d$ dimensional results reduce to previously known results in $d=4$ for 0-magnon and 1- magnon. As a non trivial check, we show that the results for 1-magnon correlator in $d=8$, when evaluated using the exact techniques in \cite{Chowdhury:2019hns, Korchemsky:2018hnb} are in perfect agreement with our $d$ dimensional perturbative results. We also perturbatively compute the Regge trajectories and Regge-Mellin amplitudes of the chiral fishnet correlator $\langle{\rm Tr}[\phi_1(x_1)\phi_1(x_2)]{\rm Tr}[\phi_1^\dagger(x_3)\phi_1^\dagger(x_4)]\rangle$ using the techniques developed in this paper. Since this correlator has two couplings $\kappa$ and $\omega$, we have obtained closed-form results in the limit $\kappa \to 0, \omega \to 0$ with $\kappa/\omega$ held constant. We verify this computation with an independent method of computing the same and obtain perfect agreement.