Heptagon Amplitude in the Multi-Regge Regime

TL;DR

This paper develops an algorithm to compute 7-gluon scattering amplitudes at strong coupling in the multi-Regge regime of N=4 supersymmetric Yang-Mills theory, connecting integrable systems with gauge theory amplitudes.

Contribution

It introduces a systematic method to calculate multi-gluon amplitudes at strong coupling using Bethe Ansatz equations, extending previous insights into integrability and scattering amplitudes.

Findings

Computed 7-gluon amplitudes at infinite 't Hooft coupling.

Results align with expected perturbative Regge cut contributions.

Demonstrated consistency with known gauge theory structures.

Abstract

As we have shown in previous work, the high energy limit of scattering amplitudes in N=4 supersymmetric Yang-Mills theory corresponds to the infrared limit of the 1-dimensional quantum integrable system that solves minimal area problems in AdS5. This insight can be developed into a systematic algorithm to compute the strong coupling limit of amplitudes in the multi-Regge regime through the solution of auxiliary Bethe Ansatz equations. We apply this procedure to compute the scattering amplitude for n=7 external gluons in different multi-Regge regions at infinite 't Hooft coupling. Our formulas are remarkably consistent with the expected form of 7-gluon Regge cut contributions in perturbative gauge theory. A full description of the general algorithm and a derivation of results will be given in a forthcoming paper.