The Imaginary Part of the N = 4 Super-Yang-Mills Two-Loop Six-Point MHV Amplitude in Multi-Regge Kinematics

TL;DR

This paper computes the imaginary part of the two-loop six-point MHV amplitude in N=4 Super-Yang-Mills theory within multi-Regge kinematics, clarifying its asymptotic behavior and confirming previous theoretical predictions.

Contribution

It provides the first precise numerical analysis of the imaginary part of the amplitude's asymptotics, supporting the non-BDS nature of the amplitude in this regime.

Findings

Numerical results align with leading-log asymptotics predictions.

The amplitude's imaginary part is not fixed by the BDS ansatz.

Supports the high-energy effective action approach.

Abstract

The precise form of the multi-Regge asymptotics of the two-loop six-point MHV amplitude in N = 4 Super-Yang-Mills theory has been a subject of recent controversy. In this paper we utilize the amplitude/Wilson loop correspondence to obtain precise numerical results for the imaginary part of these asymptotics. The region of phase-space that we consider is interesting because it allowed Bartels, Lipatov, and Sabio Vera to determine that the two-loop six-point MHV amplitude is not fixed by the BDS ansatz. They proceeded by working in the framework of a high energy effective action, thus side-stepping the need for an arduous two-loop calculation. Our numerical results are consistent with the predictions of Bartels, Lipatov, and Sabio Vera for the leading-log asymptotics.