The Gubser-Klebanov-Polyakov (GKP) string describes a rigid folded string rotating in AdS3. At large angular momentum, the GKP string is long and fluctuations can easily propagate above it. According to the AdS/CFT correspondence, this picture admits a dual description in the planar N=4 Super-Yang-Mills (SYM) theory. Namely, the long GKP string is mapped into a large-spin twist-two operator and excitations above it can be accomodated by increasing the twist of the operator. Accordingly, the analysis of the spectrum of scaling dimensions of large-spin operators give access to the spectrum of energies for excitations on top of the long GKP string. In this talk, we will explain how to obtain all-loop dispersion relations for these excitations, by considering the large-spin limit of the Beisert-Staudacher equations (conjectured to solve the spectral problem for the planar dilatation operator of the SYM theory).
