Classical/quantum integrability in non-compact sector of AdS/CFT

Abstract

We discuss non-compact SL(2,R) sectors in N=4 SYM and in AdS string theory and compare their integrable structures. We formulate and solve the Riemann-Hilbert problem for the finite gap solutions of the classical sigma model and show that at one loop it is identical to the classical limit of Bethe equations of the spin (-1/2) chain for the dilatation operator of SYM.

27 pages, 1 figure; v2: unphysical windings around the time direction eliminated; v3: dicsussion of finite-size corrections removed

References in corpus (49)

• Gauge Theory Correlators from Non-Critical String Theory
• Strings in flat space and pp waves from $\mathcal{N}=4$ Super Yang Mills
• The Bethe-Ansatz for N=4 Super Yang-Mills
• The Three-Loop Splitting Functions in QCD: The Non-Singlet Case
• Hidden Symmetries of the AdS_5 x S^5 Superstring
• 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
• Semiclassical quantization of rotating superstring in AdS_5 x S^5
• Bethe Ansatz for Quantum Strings
• Strings in AdS_3 and the SL(2,R) WZW Model. Part 1: The Spectrum
• The Complete One-Loop Dilatation Operator of N=4 Super Yang-Mills Theory
• Classical/quantum integrability in AdS/CFT
• Three-loop universal anomalous dimension of the Wilson operators in N=4 SUSY Yang-Mills model
• A Novel Long Range Spin Chain and Planar N=4 Super Yang-Mills
• Multi-spin string solutions in AdS_5 x S^5
• The su(2|3) Dynamic Spin Chain
• Stringing Spins and Spinning Strings
• Spinning strings in AdS_5 x S^5 and integrable systems
• Spinning strings in AdS_5 x S^5: new integrable system relations
• Rotating string solutions: AdS/CFT duality in non-supersymmetric sectors
• Baryon Distribution Amplitudes in QCD
• Planar N=4 gauge theory and the Inozemtsev long range spin chain
• Quantizing String Theory in AdS_5 X S^5: Beyond the pp-Wave
• Large spin limit of AdS_5 x S^5 string theory and low energy expansion of ferromagnetic spin chains
• Integrability of three-particle evolution equations in QCD
• A Relation Between Approaches to Integrability in Superconformal Yang-Mills Theory
• Matching Higher Conserved Charges for Strings and Spins
• Precision Spectroscopy of AdS/CFT
• Circular Semiclassical String Solutions on AdS_5 x S_5
• Quantizing three-spin string solution in AdS_5 x S^5
• Semiclassical relativistic strings in S^5 and long coherent operators in N=4 SYM theory
• Holography Beyond the Penrose Limit
• Renormalization of twist-three operators and integrable lattice models
• Large spin limits of AdS/CFT and generalized Landau-Lifshitz equations
• Yang-Mills Duals for Semiclassical Strings
• The SU(3) spin chain sigma model and string theory
• Conformal Fixed Points of Unidentified Gauge Theories
• Speeding Strings
• Higher Loops Beyond the SU(2) Sector
• On the Integrability of large N Plane-Wave Matrix Theory
• Pulsating Strings on AdS_5 x S^5
• New Effects in Gauge Theory from pp-wave Superstrings
• Higher Conserved Charges and Integrability for Spinning Strings in AdS_5 x S^5
• Spinning Pulsating String Solitons in AdS_5 x S^5
• Finite-Size Corrections to Anomalous Dimensions in N=4 SYM Theory
• Towards the exact dilatation operator of N=4 super Yang-Mills theory
• Supersymmetric null-surfaces
• Circular and Folded Multi-Spin Strings in Spin Chain Sigma Models

Cited by in corpus (114)

• Long-Range PSU(2,2|4) Bethe Ansaetze for Gauge Theory and Strings
• The Factorized S-Matrix of CFT/AdS
• Foundations of the AdS_5 x S^5 Superstring. Part I
• Lax Pair for Strings in Lunin-Maldacena Background
• Wrapping interactions and a new source of corrections to the spin-chain/string duality
• The Algebraic Curve of Classical Superstrings on AdS_5xS^5
• Finite-size Effects from Giant Magnons
• Quantum corrections to the string Bethe ansatz
• Integrability and the AdS(3)/CFT(2) correspondence
• Gauge-string duality for superconformal deformations of N=4 Super Yang-Mills theory
• The all loop AdS4/CFT3 Bethe ansatz
• Spinning strings and integrable spin chains in the AdS/CFT correspondence
• Logarithmic scaling in gauge/string correspondence
• Anomalous dimensions of high-spin operators beyond the leading order
• On Quantum Corrections to Spinning Strings and Bethe Equations
• Spiky strings and single trace operators in gauge theories
• Algebraic Curve for the SO(6) sector of AdS/CFT
• On Integrability of Classical SuperStrings in AdS_5 x S^5
• Logarithmic corrections to higher twist scaling at strong coupling from AdS/CFT
• The AdS5xS5 Superstring in Light-Cone Gauge and its Bethe Equations
• Extended Y-system for the $Ad{S}_5/CF{T}_4$ correspondence
• Matching quantum strings to quantum spins: one-loop vs. finite-size corrections
• The AdS4/CFT3 algebraic curve
• Infinite spin limit of semiclassical string states
• Integrability and Transcendentality
• Complete Spectrum of Long Operators in N=4 SYM at One Loop
• On the Strong Coupling Scaling Dimension of High Spin Operators
• Quantum corrections to spinning strings in AdS(5)xS(5) and Bethe ansatz: a comparative study
• On the Dynamics of Finite-Gap Solutions in Classical String Theory
• A Universality Test of the Quantum String Bethe Ansatz
• Wrapping interactions and the genus expansion of the 2-point function of composite operators
• Quantum folded string and integrability: from finite size effects to Konishi dimension
• The Bethe ansatz approach for factorizable centrally extended S-matrices
• Bethe Ansatz for a Quantum Supercoset Sigma Model
• How Accurate is the Quantum String Bethe Ansatz?
• Bethe Ansatz in Stringy Sigma Models
• The magnon kinematics of the AdS/CFT correspondence
• The AdS(5)xS(5) superstring quantum spectrum from the algebraic curve
• Y-system and Quasi-Classical Strings
• Finite-gap equations for strings on AdS_3 x S^3 x T^4 with mixed 3-form flux
• Y-system, TBA and Quasi-Classical Strings in AdS4 x CP3
• Wronskian Solution for AdS/CFT Y-system
• Quantum Wrapped Giant Magnon
• Strings as Multi-Particle States of Quantum Sigma-Models
• Finite size effects in ferromagnetic spin chains and quantum corrections to classical strings
• Exact Correlation Functions in Conformal Fishnet Theory
• Large spin corrections in $\mathcal{N}=4$ SYM sl(2): still a linear integral equation
• Comment on Strings in AdS3 x S3 x S3 x S1 at One Loop
• Deeper Look into Short Strings
• Quantum Strings and the AdS4/CFT3 Interpolating Function
• Review of AdS/CFT Integrability, Chapter II.4: The Spectral Curve
• Double Scaling and Finite Size Corrections in sl(2) Spin Chain
• Wave functions and correlation functions for GKP strings from integrability
• Integrable twists in AdS/CFT
• Surprises in the AdS algebraic curve constructions - Wilson loops and correlation functions
• Linking Backlund and Monodromy Charges for Strings on AdS_5 x S^5
• Quantum corrections to energy of short spinning string in AdS5
• Macroscopic (and Microscopic) Massless Modes
• Generalized scaling function from light-cone gauge AdS_5 x S^5 superstring
• Giant Magnon in NS5-brane Background
• Spiky strings in AdS_3 x S^1 and their AdS-pp-wave limits
• Higher Loop Bethe Ansatz for Open Spin-Chains in AdS/CFT
• Dyonic Giant Magnons in CP^3: Strings and Curves at Finite J
• Wound and Rotating Strings in AdS_5 x S^5
• Open Semiclassical Strings and Long Defect Operators in AdS/dCFT Correspondence
• Open string integrability and AdS/CFT
• From Polygon Wilson Loops to Spin Chains and Back
• The SU(2) sector in AdS/CFT
• A two-loop test for the factorised S-matrix of planar N=4
• Asymptotic Bethe Ansatz S-matrix and Landau-Lifshitz type effective 2-d actions
• Landau-Lifshitz sigma-models, fermions and the AdS/CFT correspondence
• Precision Test of AdS/CFT in Lunin-Maldacena Background
• Open Spinning Strings and AdS/dCFT Duality
• String theories on warped AdS backgrounds and integrable deformations of spin chains
• Superstring sigma models from spin chains: the SU(1,1|1) case
• A note on string solutions in AdS_3
• On the commuting charges for the highest dimension SU(2) operators in planar $\mathcal{N}=4$ SYM
• Rotating Strings with Two Unequal Spins in Lunin-Maldacena Background
• Algebraic Curves for Factorized String Solutions
• Exact form factors of the O(N) $\sigma$-model
• Spiky strings in the SL(2) Bethe Ansatz
• Sigma model from SU(1,1|2) spin chain
• Constant mean curvature surfaces in AdS_3
• Classical integrability in the BTZ black hole
• Homogeneous Yang-Baxter deformations as undeformed yet twisted models
• Anomalous dimension and local charges
• Segmented Strings in $Ad{S}_3$
• Structure constants of short operators in planar $\mathcal{N}=4$ SYM theory
• Semiclassical spectrum for BMN string in $Sc{h}_5\times S^5$
• Spiky strings in Bethe Ansatz at strong coupling
• Rational three-spin string duals and non-anomalous finite size effects
• A large spin limit of strings on AdS_5 x S^5 in a non-compact sector
• Plane wave limit of local conserved charges
• Algebraic Curves for Long Folded and Circular Winding Strings in AdS5xS5
• Current Algebra and Integrability of Principal Chiral Model on the World-sheet with General Metric
• Spiky Strings and Giant Holes
• Kinky Strings in AdS_5 x S^5
• The Anatomy of Gauge/String Duality in Lunin-Maldacena Background
• Hints of Integrability Beyond the Planar Limit: Nontrivial Backgrounds
• $A_n^{(1)}$ affine Toda field theories with integrable boundary conditions revisited
• Note About Integrability and Gauge Fixing for Bosonic String on AdS(5)xS(5)
• The S-matrix of the Faddeev-Reshetikhin Model, Diagonalizability and PT Symmetry
• On the absence of reflection in AdS4/CFT3
• Giant Holes
• Approaching the BFKL pomeron via integrable classical solutions
• Fishnet four-point integrals: integrable representations and thermodynamic limits
• Light-cone limits of large rectangular fishnets
• Wrapping effects in supersymmetric gauge theories
• Multi-Spin Strings in AdS_4*CP^3 and its β-deformation
• Comments on Correlation Functions of Large Spin Operators and Null Polygonal Wilson Loops
• Analytic Bethe Ansatz Solutions for Highest States in the su(1|1) and su(2) Sectors
• The SU(1|2) and SU(2|2) Sectors from Superstrings in AdS5 x S5
• Spiky Strings with Two Spins in AdS5
• Novel aspects of integrability for NLSMs in symmetric spaces