Exciting the GKP string at any coupling

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.

72 pages, 6 figures, references added, misprints corrected, minor revision of section 2 and 4

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• An Operator Product Expansion for Form Factors
• Hexagon OPE Resummation and Multi-Regge Kinematics
• Bethe Ansaetze for GKP strings
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• Computing Three-Point Functions for Short Operators
• Wilson loop OPE, analytic continuation and multi-Regge limit
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• Integrability in heavy quark effective theory
• Infrared properties of five-point massive amplitudes in N=4 SYM on the Coulomb branch
• Nonperturbative enhancement of superloop at strong coupling
• Towards NMHV amplitudes at strong coupling
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• All two-loop MHV remainder functions in multi-Regge kinematics
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• The four-loop six-gluon NMHV ratio function
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• Regge meets collinear in strongly-coupled $\mathcal{N}=4$ super Yang-Mills
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• Descent equation for superloop and cyclicity of OPE
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• Pohlmeyer reduction for superstrings in AdS space
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• Quantum dispersion relations for the $Ad{S}_4\times C{P}^3$ GKP string
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• A Young diagram expansion of the hexagonal Wilson loop (amplitude) in $\mathcal{N}=4$ SYM