Bethe ansätze for GKP strings

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 AdS4/CFT3AdS4/CFT3 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 AdS5/CFT4AdS5/CFT4, 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 AdS4×CP3AdS4×CP3 sigma model.