On the scattering over the GKP vacuum

TL;DR

This paper develops a method to compute 2D scattering amplitudes of excitations on the GKP vacuum in ${ m N}=4$ SYM by transforming the ABA into integral equations, revealing their dependence on a fundamental scalar-scalar amplitude.

Contribution

It introduces a non-linear integral equation framework for analyzing scattering amplitudes on the GKP vacuum, enhancing understanding of the S-matrix structure.

Findings

Derived 2D scattering amplitudes from ABA

Proved the approach's effectiveness for S-matrix computation

Showed all amplitudes depend on scalar-scalar interactions

Abstract

By converting the Asymptotic Bethe Ansatz (ABA) of ${\cal N}=4$ SYM into non-linear integral equations, we find 2D scattering amplitudes of excitations on top of the GKP vacuum. We prove that this is a suitable and powerful set-up for the understanding and computation of the whole S-matrix. We show that all the amplitudes depend on the fundamental scalar-scalar one.