Logarithmic scaling in gauge/string correspondence

Abstract

We study anomalous dimensions of (super)conformal Wilson operators at weak and strong coupling making use of the integrability symmetry on both sides of the gauge/string correspondence and elucidate the origin of their single-logarithmic behavior for long operators/strings in the limit of large Lorentz spin. On the gauge theory side, we apply the method of the Baxter Q-operator to identify different scaling regimes in the anomalous dimensions in integrable sectors of (supersymmetric) Yang-Mills theory to one-loop order and determine the values of the Lorentz spin at which the logarithmic scaling sets in. We demonstrate that the conventional semiclassical approach based on the analysis of the distribution of Bethe roots breaks down in this domain. We work out an asymptotic expression for the anomalous dimensions which is valid throughout the entire region of variation of the Lorentz spin. On the string theory side, the logarithmic scaling occurs when two most distant points of the folded spinning string approach the boundary of the AdS space. In terms of the spectral curve for the classical string sigma model, the same configuration is described by an elliptic curve with two branching points approaching values determined by the square root of the 't Hooft coupling constant. As a result, the anomalous dimensions cease to obey the BMN scaling and scale logarithmically with the Lorentz spin.

37 pages, 4 figures

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• A Test of the AdS/CFT Correspondence Using High-Spin Operators
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• 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
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• On the Strong Coupling Scaling Dimension of High Spin Operators
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• A Generalized Scaling Function for AdS/CFT
• Quantum folded string and integrability: from finite size effects to Konishi dimension
• Quantum spectral curve as a tool for a perturbative quantum field theory
• Adjoint BFKL at finite coupling: a short-cut from the collinear limit
• Spinning superstrings at two loops: strong-coupling corrections to dimensions of large-twist SYM operators
• Bootstrapping Null Polygon Wilson Loops
• Twist-three at five loops, Bethe Ansatz and wrapping
• Comment on the Scaling Function in AdS4 x CP3
• Quantization of Integrable Systems and a 2d/4d Duality
• Functional BES equation
• Embedding nonlinear O(6) sigma model into N=4 super-Yang-Mills theory
• Multipoint Bootstrap I: Light-Cone Snowflake OPE and the WL Origin
• Structure of large spin expansion of anomalous dimensions at strong coupling
• Nonsinglet pentagons and NMHV amplitudes
• Large spin corrections in $\mathcal{N}=4$ SYM sl(2): still a linear integral equation
• Scaling function in AdS/CFT from the O(6) sigma model
• Quantum integrability and functional equations
• The scaling function at strong coupling from the quantum string Bethe equations
• Long-range SL(2) Baxter equation in N=4 super-Yang-Mills theory
• Quantum mechanics of null polygonal Wilson loops
• Asymptotic Bethe Ansatz on the GKP vacuum as a defect spin chain: scattering, particles and minimal area Wilson loops
• Strong coupling for planar $\mathcal{N}=4$ SYM theory: an all-order result
• Two-loop cusp anomaly in ABJM at strong coupling
• Twist 3 of the sl(2) sector of N=4 SYM and reciprocity respecting evolution
• Quantum corrections to energy of short spinning string in AdS5
• Fine structure of anomalous dimensions in N=4 super Yang-Mills theory
• The Resurgence of the Cusp Anomalous Dimension
• The virtual scaling function of AdS/CFT
• Generalized scaling function from light-cone gauge AdS_5 x S^5 superstring
• Beyond cusp anomalous dimension from integrability
• Nonperturbative scales in AdS/CFT
• Three loop anomalous dimensions of twist-3 gauge operators in N=4 SYM
• Anomalous Dimensions from a Spinning D5-Brane
• Spiky strings in AdS_3 x S^1 and their AdS-pp-wave limits
• Large Winding Sector of AdS/CFT
• Bethe Ansaetze for GKP strings
• Anomalous dimensions at twist-3 in the sl(2) sector of N=4 SYM
• Luescher formula for GKP string
• On factorization of multiparticle pentagons
• Review of AdS/CFT Integrability, Chapter IV.4: Integrability in QCD and N<4 SYM
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• Spiky Strings and Spin Chains
• From Polygon Wilson Loops to Spin Chains and Back
• Matrix pentagons
• Reciprocity of gauge operators in N=4 SYM
• Baxter equation for long-range SL(2|1) magnet
• OPE for Super Loops
• On the scattering over the GKP vacuum
• Review of AdS/CFT Integrability, Chapter II.1: Classical AdS5xS5 string solutions
• On wrapping corrections to GKP-like operators
• Two-loop AdS_5 x S^5 superstring: testing asymptotic Bethe ansatz and finite size corrections
• The generalised scaling function: a systematic study
• OPE for null Wilson loops and open spin chains
• Strong coupling expansion of Baxter equation in N=4 SYM
• QCD properties of twist operators in the N=6 Chern-Simons theory
• Universality of three gaugino anomalous dimensions in N=4 SYM
• Spiky strings in the SL(2) Bethe Ansatz
• Scaling dimensions at small spin in N=4 SYM theory
• Aspects of Integrability in AdS/CFT Duality
• Review of AdS/CFT Integrability, Chapter II.2: Quantum Strings in AdS5xS5
• Spiky strings in Bethe Ansatz at strong coupling
• A large spin limit of strings on AdS_5 x S^5 in a non-compact sector
• Integrability in heavy quark effective theory
• Semiclassical rigid strings with two spins in AdS_5
• Algebraic Curves for Long Folded and Circular Winding Strings in AdS5xS5
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• More about "short" spinning quantum strings
• Spiky Strings and Giant Holes
• Review of AdS/CFT Integrability, Chapter III.4: Twist states and the cusp anomalous dimension
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• On the logarithmic powers of $sl(2)$ SYM${}_4$
• Large spin expansion of the long-range Baxter equation in the sl(2) sector of N=4 SYM
• Sum rules for higher twist sl(2)operators in N=4 SYM
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• From weak coupling to spinning strings
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• Analytic continuation of Bethe energies and application to the thermodynamic limit of the $SL(2,\mathbb{C})$ non-compact spin chains
• $N$-spike string in $Ad{S}_3\times S^1$ with mixed flux
• Quantum dispersion relations for the $Ad{S}_4\times C{P}^3$ GKP string
• Operator with large spin and spinning D3-brane
• Gauge-String Dualities and Some Applications
• Spiky Strings with Two Spins in AdS5
• A semiclassical analysis of the fluctuation eigenvalues and the one-loop energy of the folded spinning superstring in AdS_5 x S^5
• The CFT Distance Conjecture and Tensionless String Limits in $\mathcal{N}=2$ Quiver Gauge Theories
• Leading quantum correction to energy of "short" spiky strings
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