Exciting the GKP string at any coupling

TL;DR

This paper derives a comprehensive dispersion relation for excitations around the GKP string at any coupling, linking string theory and gauge theory spectra within the AdS/CFT framework.

Contribution

It provides a parametric representation of excitation spectra at any coupling, bridging weak and strong coupling regimes in the AdS/CFT correspondence.

Findings

Matching of dispersion relations with Frolov-Tseytlin spectrum

Identification of SO(6) symmetry restoration mechanism

Explicit analysis of spectra at various couplings

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 $\mathcal{N}=4$ 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.