Bethe Ansaetze for GKP strings

TL;DR

This paper derives the S-matrix and spectral equations for excitations around a GKP string background in AdS_4/CFT_3, showing their similarity to AdS_5/CFT_4 and reproducing known Bethe equations at strong coupling.

Contribution

It provides the first derivation of spectral equations for GKP strings in AdS_4/CFT_3, extending integrability techniques to this setting.

Findings

Spectral equations closely resemble those in AdS_5/CFT_4.

At strong coupling, equations reproduce known Bethe equations.

Derived S-matrix matches conjectured all-loop asymptotic equations.

Abstract

Studying the scattering of excitations around a dynamical background has a long history in the context of integrable models. The Gubser-Klebanov-Polyakov string solution provides such a background for the string/gauge correspondence. Taking the conjectured all-loop asymptotic equations for the AdS_4/CFT_3 correspondence as the starting point, we derive the S-matrix and a set of spectral equations for the lowest-lying excitations. We find that these equations resemble closely the analogous equations for AdS_5/CFT_4, which are also discussed in this paper. At large values of the coupling constant we show that they reproduce the Bethe equations proposed to describe the spectrum of the low-energy limit of the AdS_4xCP^3 sigma model.