Mandelstam cuts and light-like Wilson loops in N=4 SUSY

TL;DR

This paper analytically continues the two-loop six-point MHV amplitude in N=4 SUSY, revealing pure imaginary behavior in multi-Regge kinematics and confirming the Wilson loop approach's validity for these amplitudes.

Contribution

It provides the first subleading term calculation in the multi-Regge limit using Wilson loop techniques, extending previous leading-order results.

Findings

The remainder function is pure imaginary in the multi-Regge kinematics.

The leading term matches BFKL calculations.

The subleading term is a novel result not obtained by unitarity methods.

Abstract

We perform an analytic continuation of the two-loop remainder function for the six-point planar MHV amplitude in N=4 SUSY, found by Goncharov, Spradlin, Vergu and Volovich from the light-like Wilson loop representation. The remainder function is continued into a physical region, where all but two energy invariants are negative. It turns out to be pure imaginary in the multi-Regge kinematics, which is in an agreement with the predictions based on the Steinmann relations for the Regge poles and Mandelstam cut contributions. The leading term reproduces correctly the expression calculated by one of the authors in the BFKL approach, while the subleading term presents a result, that was not yet found with the use of the unitarity techniques. This supports the applicability of the Wilson loop approach to the planar MHV amplitudes in N=4 SUSY.