Towards integrability for AdS3/CFT2

Abstract

We review the recent progress towards applying worldsheet integrability techniques to the $Ad{S}_3/CF{T}_2$ correspondence to find its all-loop S matrix and Bethe-Yang equations. We study in full detail the massive sector of $Ad{S}_3\times S^3\times T^4$ superstrings supported by pure Ramond-Ramond (RR) fluxes. The extension of this machinery to accommodate massless modes, to the $Ad{S}_3\times S^3\times S^3\times S^1$ pure-RR background and to backgrounds supported by mixed background fluxes is also reviewed. While the results discussed here were found elsewhere, our presentation sometimes deviates from the one found in the original literature in an effort to be pedagogical and self-contained.

Review, 152 pages, 29 figures; v2: minor changes, references added; v3: more minor changes, more references; v4: misprints corrected, references updated, as published

References in corpus (163)

• Gauge Theory Correlators from Non-Critical String Theory
• Large N Field Theories, String Theory and Gravity
• The World as a Hologram
• The Black Hole in Three Dimensional Space Time
• Microscopic Origin of the Bekenstein-Hawking Entropy
• Geometry of the 2+1 Black Hole
• Black Hole Entropy from Near-Horizon Microstates
• Hidden Symmetries of the AdS_5 x S^5 Superstring
• Type IIB superstring action in AdS_5 x S^5 background
• The N=4 SYM Integrable Super Spin Chain
• The Dilatation Operator of Conformal N=4 Super Yang-Mills Theory
• 4d Conformal Field Theories and Strings on Orbifolds
• Deforming field theories with $U(1)\times U(1)$ global symmetry and their gravity duals
• Long-Range PSU(2,2|4) Bethe Ansaetze for Gauge Theory and Strings
• W-symmetry in Conformal Field Theory
• Massless Higher Spins and Holography
• The (2+1)-Dimensional Black Hole
• Strings in AdS_3 and the SL(2,R) WZW Model. Part 1: The Spectrum
• Asymptotic symmetries of three-dimensional gravity coupled to higher-spin fields
• On Conformal Theories in Four Dimensions
• Nonlinear W(infinity) Algebra as Asymptotic Symmetry of Three-Dimensional Higher Spin Anti-de Sitter Gravity
• The Complete One-Loop Dilatation Operator of N=4 Super Yang-Mills Theory
• Matrix Description of M-theory on $T^5$ and $T^5/Z_2$
• An AdS_3 Dual for Minimal Model CFTs
• Giant Magnons
• The su(2|2) Dynamic S-Matrix
• High energy QCD as a completely integrable model
• The AdS_5xS^5 superstring worldsheet S-matrix and crossing symmetry
• The Dilatation Operator of N=4 Super Yang-Mills Theory and Integrability
• Microscopic Formulation of Black Holes in String Theory
• Integrability for the Full Spectrum of Planar AdS/CFT II
• The su(2|3) Dynamic Spin Chain
• Integrability for the Full Spectrum of Planar AdS/CFT
• Spin chains and string theory
• Six-Dimensional Supergravity on S^3 X AdS_3 and 2d Conformal Field Theory
• Quantum spectral curve for AdS_5/CFT_4
• More Comments on String Theory on AdS_3
• Conformal Field Theory of AdS Background with Ramond-Ramond Flux
• Stringy gravity, interacting tensionless strings and massless higher spins
• Spinning strings in AdS_5 x S^5 and integrable systems
• Wrapping interactions and a new source of corrections to the spin-chain/string duality
• Spinning strings in AdS_5 x S^5: new integrable system relations
• Symmetries of Holographic Minimal Models
• Four-loop perturbative Konishi from strings and finite size effects for multiparticle states
• Strings in AdS_3 and the SL(2,R) WZW Model. Part 3: Correlation Functions
• Green-Schwarz action for Type IIA strings on $Ad{S}_4\times C{P}^3$
• Finite-size Effects from Giant Magnons
• Black Holes and Solitons in String Theory
• Large spin limit of AdS_5 x S^5 string theory and low energy expansion of ferromagnetic spin chains
• An exact formula for the radiation of a moving quark in N=4 super Yang Mills
• String Lessons for Higher-Spin Interactions
• Instantons on D-branes
• The Bethe ansatz for superconformal Chern-Simons
• Integrability and the AdS(3)/CFT(2) correspondence
• S-matrix for strings on $\eta$-deformed AdS5 x S5
• Jordanian deformations of the AdS_5xS^5 superstring
• Supersymmetry of the 2+1 black holes
• The SU(2) x SU(2) sector in the string dual of N=6 superconformal Chern-Simons theory
• The quark anti-quark potential and the cusp anomalous dimension from a TBA equation
• Exact AdS/CFT spectrum: Konishi dimension at any coupling
• The Off-shell Symmetry Algebra of the Light-cone AdS_5 x S^5 Superstring
• Spin Chains in N=6 Superconformal Chern-Simons-Matter Theory
• Diagrams for Symmetric Product Orbifolds
• Light-cone Superstring in AdS Space-time
• Thermodynamic Bethe Ansatz for planar AdS/CFT: a proposal
• Magnon Bound States and the AdS/CFT Correspondence
• Quantum Deformations of the One-Dimensional Hubbard Model
• On The Conformal Field Theory Of The Higgs Branch
• Instanton Strings and HyperKaehler Geometry
• On the Singularities of the Magnon S-matrix
• B-field in AdS(3)/CFT(2) Correspondence and Integrability
• The Holographic Dual of AdS3 x S3 x S3 x S1
• Large N=4 Holography
• The all-loop integrable spin-chain for strings on AdS_3 x S^3 x T^4: the massive sector
• On string theory on AdS_3 x S^3 x T^4 with mixed 3-form flux: tree-level S-matrix
• Strings on Semisymmetric Superspaces
• Three-dimensional N=6 SCFT's and their membrane dynamics
• A dynamic su(1|1)^2 S-matrix for AdS3/CFT2
• The AdS5xS5 Superstring in Light-Cone Gauge and its Bethe Equations
• The complete AdS_3 x S^3 x T^4 worldsheet S-matrix
• Supersymmetry of Rotating Branes
• Extended Y-system for the $Ad{S}_5/CF{T}_4$ correspondence
• Giant magnon solution and dispersion relation in string theory in AdS_3 x S^3 x T^4 with mixed flux
• Review of AdS/CFT Integrability, Chapter IV.3: N=6 Chern-Simons and Strings on AdS4xCP3
• On the Hopf algebra structure of the AdS/CFT S-matrix
• String Theory in Magnetic Monopole Backgrounds
• The S-matrix of String Bound States
• Connecting giant magnons to the pp-wave: An interpolating limit of $Ad{S}_5\times S^5$
• Integrability, spin-chains and the AdS3/CFT2 correspondence
• The Quantum Spectral Curve of the ABJM theory
• All-loop Bethe ansatz equations for AdS3/CFT2
• Super-W(infinity) Asymptotic Symmetry of Higher-Spin AdS(3) Supergravity
• Classical integrability and quantum aspects of the AdS(3) x S(3) x S(3) x S(1) superstring
• Dressing phases of AdS3/CFT2
• A Spin Chain for the Symmetric Product CFT_2
• Long-Range Deformations for Integrable Spin Chains
• Five-loop Konishi from the Mirror TBA
• String Theory on AdS_3 x S^3 x S^3 x S^1
• Analytic Solution of Bremsstrahlung TBA
• q-Deformation of the AdS5 x S5 Superstring S-matrix and its Relativistic Limit
• Exact Slope and Interpolating Functions in ABJM Theory
• Review of AdS/CFT Integrability, Chapter VI.1: Superconformal Symmetry
• Near BMN dynamics of the AdS(3) x S(3) x S(3) x S(1) superstring
• Worldsheet scattering in AdS(3)/CFT(2)
• Quantum corrections to spinning superstrings in AdS_3 x S^3 x M^4: determining the dressing phase
• TBA and Y-system for planar $Ad{S}_4/CF{T}_3$
• Matching of correlators in AdS_3/CFT_2
• Towards the quantum S-matrix of the Pohlmeyer reduced version of AdS_5 x S^5 superstring theory
• $Ad{S}_3\times S^3\times M^4$ string S-matrices from unitarity cuts
• Integrability of scattering amplitudes in N=4 SUSY
• The GS String Action on AdS(3)xS(3) with Ramond-Ramond Charge
• S-matrix for magnons in the D1-D5 system
• Exploring the mirror TBA
• Integrability of the AdS_5 x S^5 superstring and its deformations
• Review of AdS/CFT Integrability, Chapter IV.2: Deformations, Orbifolds and Open Boundaries
• Duality symmetry of Reggeon interactions in multicolour QCD
• Supersymmetric spacetimes in 2+1 adS-supergravity models
• Y-system, TBA and Quasi-Classical Strings in AdS4 x CP3
• The GS Type IIB Superstring Action on AdS(3) X S(3) X T(4)
• Two-dimensional S-matrices from unitarity cuts
• Quantum Wrapped Giant Magnon
• Konishi operator at intermediate coupling
• Multiple zeta functions and double wrapping in planar N=4 SYM
• Exact N=4 correlators of AdS(3)/CFT(2)
• 5-loop Konishi from linearized TBA and the XXX magnet
• Long-Range GL(n) Integrable Spin Chains and Plane-Wave Matrix Theory
• Massless Flows I: the sine-Gordon and O(n) models
• Comment on Strings in AdS3 x S3 x S3 x S1 at One Loop
• Evidence for the classical integrability of the complete AdS(4) x CP(3) superstring
• Supersymmetric holography on AdS3
• $Ad{S}_3/CF{T}_2$, finite-gap equations and massless modes
• Review of AdS/CFT Integrability, Chapter III.3: The dressing factor
• Super spin chain coherent state actions and $Ad{S}_5\times S^5$ superstring
• $Ad{S}_5\times S^5$ mirror TBA equations from Y-system and discontinuity relations
• Yangians, S-matrices and AdS/CFT
• Superparticle and superstring in AdS_3 x S^3 Ramond-Ramond background in light-cone gauge
• Secret Symmetries of Type IIB Superstring Theory on AdS3 x S3 x M4
• Quantum corrections to short folded superstring in AdS_3 x S^3 x M^4
• Worldsheet two- and four-point functions at one loop in AdS(3) / CFT(2)
• Exact S-matrices for AdS_3/CFT_2
• Dyonic Giant Magnons in CP^3: Strings and Curves at Finite J
• Hybrid-NLIE for the AdS/CFT spectral problem
• Six-loop Konishi anomalous dimension from the Y-system
• The AdS3 x S3 x S3 x S1 Hernandez-Lopez Phases: a Semiclassical Derivation
• Exact S-Matrices with Affine Quantum Group Symmetry
• Supergeometry of Three Dimensional Black Holes
• The massless string spectrum on AdS_3 x S^3 from the supergroup
• The low energy limit of the AdS(3) x S(3) x M(4) spinning string
• Comments on the Mirror TBA
• Hybrid NLIE for the Mirror AdS_5 x S^5
• Supersymmetric Giant Graviton Solutions in AdS_3
• Exceptional Operators in N=4 super Yang-Mills
• Classical and quantum integrability in AdS(2)/CFT(1)
• The Bound State S-matrix of the Deformed Hubbard Chain
• Classical integrability in the BTZ black hole
• Review of AdS/CFT Integrability, Chapter I.3: Long-range spin chains
• Lifting asymptotic degeneracies with the Mirror TBA
• Bound States in the Mirror TBA
• Superstrings in AdS in light cone gauge
• On string integrability. A journey through the two-dimensional hidden symmetries in the AdS/CFT dualities
• Off-shell symmetry algebra of the AdS_4 x CP^3 superstring
• Generating string solutions in BTZ
• S-duality and the giant magnon dispersion relation

Cited by in corpus (54)

• Strings on NS-NS Backgrounds as Integrable Deformations
• Integrable spin chain for stringy Wess-Zumino-Witten models
• $T\bar{T}$ deformations with $\mathcal{N}=(0,2)$ supersymmetry
• $T\bar{T}$ deformations and integrable spin chains
• An Integrability Primer for the Gauge-Gravity Correspondence: an Introduction
• On the Dressing Factors, Bethe Equations and Yangian Symmetry of Strings on AdS3 x S3 x T4
• Massless Lüscher Terms and the Limitations of the AdS3 Asymptotic Bethe Ansatz
• $T\bar{T}$ deformations as TsT transformations
• Integrability in dipole-deformed N=4 super Yang-Mills
• The Worldsheet Dual of Free Super Yang-Mills in 4D
• Classifying nearest-neighbour interactions and deformations of AdS
• On the Classical Integrability of Root-$T\overline{T}$ Flows
• New Dressing Factors for AdS3/CFT2
• Quasi-local holographic dualities in non-perturbative 3d quantum gravity
• One- and two-loop checks for the AdS(3) x S(3) x T(4) superstring with mixed flux
• Mirror Thermodynamic Bethe Ansatz for AdS3/CFT2
• On the spectrum of AdS3 x S3 x T4 strings with Ramond-Ramond flux
• Lectures on S-matrices and Integrability
• Elliptic solutions in the Neumann-Rosochatius system with mixed flux
• Generalized BRST symmetry for arbitrary spin conformal field theory
• Integrable open spin-chains in AdS3/CFT2 correspondences
• Free Fermions, vertex Hamiltonians, and lower-dimensional AdS/CFT
• A review of the AdS/CFT Quantum Spectral Curve
• Massless S matrices for AdS3/CFT2
• Positivity of hexagon perturbation theory
• Massless sector of AdS_3 superstrings: a geometric interpretation
• The plane-wave spectrum from the worldsheet
• Integrable supersymmetric deformations of $\mathrm{Ad}{\mathrm{S}}_3\times {\mathrm{S}}^3\times {\mathrm{T}}^4$
• Integrable bootstrap for AdS3/CFT2 correlation functions
• Coset space actions for nonrelativistic strings
• Massless $Ad{S}_2$ scattering and Bethe ansatz
• The Tensionless Limit of Pure-Ramond-Ramond AdS3/CFT2
• String theory in AdS_3 x S^3 x T^4 with mixed flux: semiclassical and 1-loop phase in the S-matrix
• Integrable deformations of AdS/CFT
• Superstrings in Thermal Anti-de Sitter Space
• Boost generator in AdS_3 integrable superstrings for general braiding
• $q$-Poincaré invariance of the $Ad{S}_3/CF{T}_2$ $R$-matrix
• S matrix for a three-parameter integrable deformation of $Ad{S}_3\times S^3$ strings
• Integrability of D1-brane on Group Manifold with Mixed Three Form Flux
• Coset construction of AdS particle dynamics
• A study of integrable form factors in massless relativistic AdS_3
• Three-parameter deformation of $\mathbb{R}\times S^3$ in the Landau-Lifshitz limit
• On $Ad{S}_2/CF{T}_1$ transfer matrices, Bethe ansatz and scale invariance
• Perturbed symmetric-product orbifold: first-order mixing and puzzles for integrability
• On N-spike strings in conformal gauge with NS-NS fluxes
• Mellin amplitudes for $Ad{S}_3\times S^3$
• $Ad{S}_3\times S^3$ Background from Poisson-Lie T-Duality
• Remarks on BMS${}_3$ invariant field theories: correlation functions and nonunitary CFTs
• Hexagonalization in $Ad{S}_3\times S^3\times T^4$: Mirror Corrections
• $N$-spike string in $Ad{S}_3\times S^1$ with mixed flux
• N spike D-strings in AdS Space with mixed flux
• Neumann-Rosochatius system for strings on I-brane
• Transfer matrices for AdS3/CFT2
• Neumann-Rosochatius system for rotating strings in $Ad{S}_3\times S^3\times S^3\times S^1$ with flux