A Test of the AdS/CFT Correspondence Using High-Spin Operators

Abstract

In two remarkable recent papers, hep-th/0610248 and hep-th/0610251, the complete planar perturbative expansion was proposed for the universal function of the coupling, f(g), appearing in the dimensions of high-spin operators of the N=4 SYM theory. We study numerically the integral equation derived in hep-th/0610251, which implements a resummation of the perturbative expansion, and find a smooth function that approaches the asymptotic form predicted by string theory. In fact, the two leading terms at strong coupling match with high accuracy the results obtained for the semiclassical folded string spinning in $Ad{S}_5$. This constitutes a remarkable confirmation of the AdS/CFT correspondence for high-spin operators, and equivalently for the cusp anomaly of a Wilson loop. We also make a numerical prediction for the third term in the strong coupling series.

11 pages, 1 figure; added references, corrected typos

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Cited by in corpus (110)

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• Comments on gluon scattering amplitudes via AdS/CFT
• Hexagon Wilson loop = six-gluon MHV amplitude
• The Two-Loop Six-Gluon MHV Amplitude in Maximally Supersymmetric Yang-Mills Theory
• Comments on operators with large spin
• Maximally Supersymmetric Planar Yang-Mills Amplitudes at Five Loops
• The Zamolodchikov-Faddeev Algebra for AdS_5 x S^5 Superstring
• A supermatrix model for N=6 super Chern-Simons-matter theory
• On String S-matrix, Bound States and TBA
• Scattering Amplitudes, Wilson Loops and the String/Gauge Theory Correspondence
• Cusp anomalous dimension in maximally supersymmetric Yang-Mills theory at strong coupling
• Space-time S-matrix and Flux tube S-matrix II. Extracting and Matching Data
• Supersymmetric Wilson loops on S^3
• Four loop twist two, BFKL, wrapping and strings
• Two-loop world-sheet corrections in AdS_5 x S^5 superstring
• Space-time S-matrix and Flux-tube S-matrix III. The two-particle contributions
• Logarithmic corrections to higher twist scaling at strong coupling from AdS/CFT
• Semiclassical Quantization of Spinning Strings in AdS_4 x CP^3
• Space-time S-matrix and Flux-tube S-matrix IV. Gluons and Fusion
• Four-Loop Cusp Anomalous Dimension From Obstructions
• On the Strong Coupling Scaling Dimension of High Spin Operators
• The Strong Coupling Limit of the Scaling Function from the Quantum String Bethe Ansatz
• Exciting the GKP string at any coupling
• A Generalized Scaling Function for AdS/CFT
• Quantum folded string and integrability: from finite size effects to Konishi dimension
• Strong-coupling expansion of cusp anomaly from quantum superstring
• Quantum spectral curve as a tool for a perturbative quantum field theory
• Strong coupling limit of Bethe Ansatz equations
• Spinning superstrings at two loops: strong-coupling corrections to dimensions of large-twist SYM operators
• Nine-Propagator Master Integrals for Massless Three-Loop Form Factors
• The Origin of the Six-Gluon Amplitude in Planar $\mathcal{N}=4$ SYM
• Embedding nonlinear O(6) sigma model into N=4 super-Yang-Mills theory
• Functional BES equation
• Nonsinglet pentagons and NMHV amplitudes
• On Drinfeld's second realization of the AdS/CFT su(2|2) Yangian
• Quantum integrability and functional equations
• Scaling function in AdS/CFT from the O(6) sigma model
• Supersymmetric Wilson loops at two loops
• Classical r-matrix of the su(2|2) SYM spin-chain
• Spiky strings, light-like Wilson loops and pp-wave anomaly
• The scaling function at strong coupling from the quantum string Bethe equations
• A Secret Symmetry of the AdS/CFT S-matrix
• Finite Size Giant Magnon
• Analytic three-loop Solutions for N=4 SYM Twist Operators
• Review of AdS/CFT Integrability, Chapter III.3: The dressing factor
• Strong coupling for planar $\mathcal{N}=4$ SYM theory: an all-order result
• A Yangian Double for the AdS/CFT Classical r-matrix
• Four-Loop Collinear Anomalous Dimension in N = 4 Yang-Mills Theory
• Duality between Wilson loops and gluon amplitudes
• Resurgence of the Cusp Anomalous Dimension
• All-order amplitudes at any multiplicity in the multi-Regge limit
• Nonperturbative Negative Geometries: Amplitudes at Strong Coupling and the Amplituhedron
• Pomeron in the N=4 supersymmetric gauge model at strong couplings
• Fine structure of anomalous dimensions in N=4 super Yang-Mills theory
• On Symmetry Enhancement in the psu(1,1|2) Sector of N=4 SYM
• Reduced sigma-model on AdS_5 x S^5: one-loop scattering amplitudes
• The Resurgence of the Cusp Anomalous Dimension
• UV finiteness of Pohlmeyer-reduced form of the AdS_5xS^5 superstring theory
• Generalized scaling function from light-cone gauge AdS_5 x S^5 superstring
• Beyond cusp anomalous dimension from integrability
• Nonperturbative scales in AdS/CFT
• Spiky strings in AdS_3 x S^1 and their AdS-pp-wave limits
• Anomalous dimensions at twist-3 in the sl(2) sector of N=4 SYM
• Zero modes for the giant magnon
• Yangian Symmetry and Integrability of Planar N=4 Super-Yang-Mills Theory
• Luescher formula for GKP string
• The generalised scaling function: a note
• Conformal SO(2,4) Transformations of the One-Cusp Wilson Loop Surface
• Factorized world-sheet scattering in near-flat AdS_5 x S^5
• Quark scattering amplitudes at strong coupling
• Superspace calculation of the three-loop dilatation operator of N=4 SYM theory
• Reciprocity of gauge operators in N=4 SYM
• Analyticity of the Free Energy of a Closed 3-Manifold
• Strong coupling expansion of Baxter equation in N=4 SYM
• What can we learn about QCD and collider physics from N=4 super Yang-Mills?
• The generalised scaling function: a systematic study
• Fusion hierarchies for N = 4 superYang-Mills theory
• The su(2|3) Undynamic Spin Chain
• Spiky strings in the SL(2) Bethe Ansatz
• Spiky strings in Bethe Ansatz at strong coupling
• Implementation of the Duality between Wilson loops and Scattering Amplitudes in QCD
• Structure of the string R-matrix
• Algebraic Curves for Long Folded and Circular Winding Strings in AdS5xS5
• The 2-loop generalized scaling function from the BES/FRS equation
• The property of maximal transcendentality: calculation of master integrals
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• On the high spin expansion in the $sl(2)$ $\mathcal{N}=4$ SYM theory
• On the logarithmic powers of $sl(2)$ SYM${}_4$
• The SAGEX Review on Scattering Amplitudes, Chapter 15: The Multi-Regge Limit
• The property of maximal transcendentality: calculation of Feynman integrals
• Parton Energy Loss in Strongly Coupled AdS/CFT
• Large spin behavior of anomalous dimensions and short-long strings duality
• TBA-like equations and Casimir effect in (non-)perturbative AdS/CFT
• An Origin Story for Amplitudes
• Strings for Quantumchromodynamics
• Generalized Gribov-Lipatov Reciprocity and AdS/CFT
• The high spin expansion of twist sector dimensions: the planar N=4 super Yang-Mills theory
• Microscopic formulation of the S-matrix in AdS/CFT
• Twistors, strings and supersymmetric gauge theories
• Aspects of Integrability in N =4 SYM
• Anomalous dimensions from rotating open strings in AdS/CFT
• DGLAP and BFKL equations in $\mathcal{N}=4$ SYM: from weak to strong coupling
• Gauge-String Dualities and Some Applications
• Analytic Bethe Ansatz Solutions for Highest States in the su(1|1) and su(2) Sectors
• Operator with large spin and spinning D3-brane
• All-order results for soft and collinear gluons
• Spiky Strings with Two Spins in AdS5
• Pomeron in the N=4 SYM at strong couplings
• A semiclassical analysis of the fluctuation eigenvalues and the one-loop energy of the folded spinning superstring in AdS_5 x S^5
• Topics in Cusped/Lightcone Wilson Loops