Abstract :
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 image 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 image symmetry, initially broken by the choice of the Berenstein–Maldacena–Nastase vacuum in the Bethe ansatz solution to the mixing problem.
