On the scattering over the GKP vacuum

TL;DR

This work develops a non-perturbative framework for computing 2D scattering amplitudes of excitations on the GKP vacuum in N=4 SYM by converting the Beisert-Staudacher ABA into nonlinear integral equations. It demonstrates that all scattering phases factorize to depend solely on the fundamental scalar-scalar amplitude, with the matrix structure fixed by residual su(4) symmetry, and provides explicit formulas for scalar, gluon, and fermion sectors. One-loop results and strong-coupling analyses are presented, with key findings in agreement with the BSV conjectures. The approach offers a powerful, unified method to obtain the full S-matrix of excitations on the GKP string, with potential applicability to broader operator sectors.

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.