  We analyze the spectrum of excitations around the Gubser-Klebanov-Polyakov
(GKP) rotating string in the long string limit and construct a parametric
representation for their dispersion relations at any value of the string
tension. On the gauge theory side of the AdS/CFT correspondence, i.e., in the
planar $\mathcal{N}=4$ Super-Yang-Mills theory, the problem is equivalent to
finding the spectrum of scaling dimensions of large spin, single-trace
operators. Their scaling dimensions are obtained from the analysis of the
Beisert-Staudacher asymptotic Bethe ansatz equations, which are believed to
solve the spectral problem of the planar gauge theory. We examine the resulting
dispersion relations in various kinematical regimes, both at weak and strong
coupling, and detail the matching with the Frolov-Tseytlin spectrum of
transverse fluctuations of the long GKP string. At a more dynamical level, we
identify the mechanism for the restoration of the SO(6) symmetry, initially
broken by the choice of the Berenstein-Maldacena-Nastase vacuum in the Bethe
ansatz solution to the mixing problem.
