The Strong Coupling Limit of the Scaling Function from the Quantum String Bethe Ansatz

Abstract

Using the quantum string Bethe ansatz we derive the one-loop energy of a folded string rotating with angular momenta (S,J) in AdS_3 x S^1 inside AdS_5 x S^5 in the limit 1 << J << S, z=λ^(1/2) log(S/J) /(πJ) fixed. The one-loop energy is a sum of two contributions, one originating from the Hernandez-Lopez phase and another one being due to spin chain finite size effects. We find a result which at the functional level exactly matches the result of a string theory computation. Expanding the result for large z we obtain the strong coupling limit of the scaling function for low twist, high spin operators of the SL(2) sector of N=4 SYM. In particular we recover the famous -3 log(2)/π. Its appearance is a result of non-trivial cancellations between the finite size effects and the Hernandez-Lopez correction.

18 pages, one figure, v2: footnote changed, v3: reference added, typo corrected

References in corpus (27)

• The Bethe-Ansatz for N=4 Super Yang-Mills
• A semi-classical limit of the gauge/string correspondence
• The N=4 SYM Integrable Super Spin Chain
• The Dilatation Operator of Conformal N=4 Super Yang-Mills Theory
• Long-Range PSU(2,2|4) Bethe Ansaetze for Gauge Theory and Strings
• Semiclassical quantization of rotating superstring in AdS_5 x S^5
• Bethe Ansatz for Quantum Strings
• The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory
• Multi-spin string solutions in AdS_5 x S^5
• The Factorized S-Matrix of CFT/AdS
• A Crossing-Symmetric Phase for AdS_5 x S^5 Strings
• Aspects of Semiclassical Strings in AdS${}_5$
• Quantum corrections to the string Bethe ansatz
• Precision Spectroscopy of AdS/CFT
• Logarithmic scaling in gauge/string correspondence
• A Test of the AdS/CFT Correspondence Using High-Spin Operators
• On the highest transcendentality in N=4 SUSY
• Two-loop world-sheet corrections in AdS_5 x S^5 superstring
• Logarithmic corrections to higher twist scaling at strong coupling from AdS/CFT
• Exact Solution of the O(n) Model on a Random Lattice
• Matching quantum strings to quantum spins: one-loop vs. finite-size corrections
• Multicritical Phases of the O(n) Model on a Random Lattice
• On the Strong Coupling Scaling Dimension of High Spin Operators
• A Universality Test of the Quantum String Bethe Ansatz
• More on the exact solution of the O(n) model on a random lattice and an investigation of the case |n|>2
• Finite size effects in ferromagnetic spin chains and quantum corrections to classical strings
• The scaling function at strong coupling from the quantum string Bethe equations

Cited by in corpus (74)

• The Two-Loop Six-Gluon MHV Amplitude in Maximally Supersymmetric Yang-Mills Theory
• Comments on operators with large spin
• On String S-matrix, Bound States and TBA
• Cusp anomalous dimension in maximally supersymmetric Yang-Mills theory at strong coupling
• Four loop twist two, BFKL, wrapping and strings
• Quantum spinning strings in AdS_4 x CP^3: testing the Bethe Ansatz proposal
• Semiclassical Quantization of Spinning Strings in AdS_4 x CP^3
• Exciting the GKP string at any coupling
• A Generalized Scaling Function for AdS/CFT
• Complete 1-loop test of AdS/CFT
• Quantum folded string and integrability: from finite size effects to Konishi dimension
• The Dressing Factor and Crossing Equations
• Quantum corrections to spinning superstrings in AdS_3 x S^3 x M^4: determining the dressing phase
• Spinning superstrings at two loops: strong-coupling corrections to dimensions of large-twist SYM operators
• Comment on the Scaling Function in AdS4 x CP3
• Generalized cusp in AdS_4 x CP^3 and more one-loop results from semiclassical strings
• Embedding nonlinear O(6) sigma model into N=4 super-Yang-Mills theory
• Functional BES equation
• Multiple zeta functions and double wrapping in planar N=4 SYM
• Structure of large spin expansion of anomalous dimensions at strong coupling
• On Drinfeld's second realization of the AdS/CFT su(2|2) Yangian
• Scaling function in AdS/CFT from the O(6) sigma model
• Quantum integrability and functional equations
• Comment on Strings in AdS3 x S3 x S3 x S1 at One Loop
• Quantum AdS_5 x S^5 superstring in the AdS light-cone gauge
• Review of AdS/CFT Integrability, Chapter III.3: The dressing factor
• Analytic three-loop Solutions for N=4 SYM Twist Operators
• Strong coupling for planar $\mathcal{N}=4$ SYM theory: an all-order result
• Four-Loop Collinear Anomalous Dimension in N = 4 Yang-Mills Theory
• On Symmetry Enhancement in the psu(1,1|2) Sector of N=4 SYM
• Fine structure of anomalous dimensions in N=4 super Yang-Mills theory
• The virtual scaling function of AdS/CFT
• 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
• Nonperturbative scales in AdS/CFT
• Large Winding Sector of AdS/CFT
• Spiky strings in AdS_3 x S^1 and their AdS-pp-wave limits
• Bethe Ansaetze for GKP strings
• Luescher formula for GKP string
• The generalised scaling function: a note
• From Polygon Wilson Loops to Spin Chains and Back
• Factorized world-sheet scattering in near-flat AdS_5 x S^5
• Quark scattering amplitudes at strong coupling
• Reciprocity of gauge operators in N=4 SYM
• Superspace calculation of the three-loop dilatation operator of N=4 SYM theory
• Strong coupling expansion of Baxter equation in N=4 SYM
• Two-loop AdS_5 x S^5 superstring: testing asymptotic Bethe ansatz and finite size corrections
• The generalised scaling function: a systematic study
• Spiky strings in the SL(2) Bethe Ansatz
• Quantum dispersion relations for excitations of long folded spinning superstring in AdS_5 x S^5
• 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
• 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
• Review of AdS/CFT Integrability, Chapter III.4: Twist states and the cusp anomalous dimension
• Towards NMHV amplitudes at strong coupling
• On the high spin expansion in the $sl(2)$ $\mathcal{N}=4$ SYM theory
• Large spin expansion of the long-range Baxter equation in the sl(2) sector of N=4 SYM
• On the logarithmic powers of $sl(2)$ SYM${}_4$
• Anomalous dimensions of finite size field strength operators in N=4 SYM
• TBA-like equations and Casimir effect in (non-)perturbative AdS/CFT
• Generalized Gribov-Lipatov Reciprocity and AdS/CFT
• The high spin expansion of twist sector dimensions: the planar N=4 super Yang-Mills theory
• Fishnet four-point integrals: integrable representations and thermodynamic limits
• On the dressing phase in the SL(2) Bethe Ansatz
• Light-cone limits of large rectangular fishnets
• Microscopic formulation of the S-matrix in AdS/CFT
• DGLAP and BFKL equations in $\mathcal{N}=4$ SYM: from weak to strong coupling
• Generalised scaling at subleading order
• Operator with large spin and spinning D3-brane
• Beyond cusp anomalous dimension from integrability in SYM${}_4$
• Spiky Strings with Two Spins in AdS5