Integrability for the Full Spectrum of Planar AdS/CFT II

Abstract

Using the thermodynamical Bethe ansatz method we derive an infinite set of integral non-linear equations for the spectrum of states/operators in AdS/CFT. The Y-system conjectured in arXiv:0901.3753 for the spectrum of all operators in planar N=4 SYM theory follows from these equations. In particular, we present the integral equations for the spectrum of all operators within the sl(2) sector. We prove that all the kernels and free terms entering these TBA equations are real and have nice fusion properties in the relevant mirror kinematics. We find the analogue of DHM formula for the dressing kernel in the mirror kinematics.

Journal version

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• The AdS_5xS^5 superstring worldsheet S-matrix and crossing symmetry
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• The Bethe ansatz for superconformal Chern-Simons
• On String S-matrix, Bound States and TBA
• The all loop AdS4/CFT3 Bethe ansatz
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• On the Singularities of the Magnon S-matrix
• Supersymmetric Bethe Ansatz and Baxter Equations from Discrete Hirota Dynamics
• Anomalous dimension with wrapping at four loops in N=4 SYM
• The AdS4/CFT3 algebraic curve
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Cited by in corpus (280)

• Foundations of the AdS_5 x S^5 Superstring. Part I
• Thermodynamic Bethe Ansatz for the AdS_5 x S^5 Mirror Model
• Quantum spectral curve for AdS_5/CFT_4
• Thermodynamic Bubble Ansatz
• Y-system for Scattering Amplitudes
• Integrability and the AdS(3)/CFT(2) correspondence
• The quark anti-quark potential and the cusp anomalous dimension from a TBA equation
• New integrable non-gauge 4D QFTs from strongly deformed planar N=4 SYM
• Superconformal symmetry and two-loop amplitudes in planar N=4 super Yang-Mills
• Quantum spectral curve for arbitrary state/operator in AdS${}_5$/CFT${}_4$
• A Shortcut to the Q-Operator
• On three-point correlation functions in the gauge/gravity duality
• The complete worldsheet S matrix of superstrings on AdS_3 x S^3 x T^4 with mixed three-form flux
• Five-Loop Anomalous Dimension of Twist-Two Operators
• Strings on Semisymmetric Superspaces
• Five loop Konishi from AdS/CFT
• Integrable Wilson loops
• The complete AdS_3 x S^3 x T^4 worldsheet S-matrix
• Exacting N=4 Superconformal Symmetry
• Extended Y-system for the $Ad{S}_5/CF{T}_4$ correspondence
• Review of AdS/CFT Integrability, Chapter IV.3: N=6 Chern-Simons and Strings on AdS4xCP3
• Integrable deformations of T-dual $\sigma$ models
• On correlation functions of operators dual to classical spinning string states
• On the exact spectrum and mirror duality of the (AdS_5 x S^5)_eta superstring
• Exciting the GKP string at any coupling
• Quantum Spectral Curve and the Numerical Solution of the Spectral Problem in AdS5/CFT4
• T-system on T-hook: Grassmannian Solution and Twisted Quantum Spectral Curve
• Five-loop Konishi from the Mirror TBA
• A Spin Chain for the Symmetric Product CFT_2
• Analytic Solution of Bremsstrahlung TBA
• Towards integrability for AdS3/CFT2
• Quantum folded string and integrability: from finite size effects to Konishi dimension
• q-Deformation of the AdS5 x S5 Superstring S-matrix and its Relativistic Limit
• Simplifying superstring and D-brane actions in AdS(4) x CP(3) superbackground
• Solving the AdS/CFT Y-system
• Quantum spectral curve as a tool for a perturbative quantum field theory
• The ${\mathrm{AdS}}_5\times {\mathrm{S}}^5$ mirror model as a string
• Correlation functions of three heavy operators - the AdS contribution
• The Dressing Factor and Crossing Equations
• BPS Wilson loops and Bremsstrahlung function in ABJ(M): a two loop analysis
• Solutions of the T-system and Baxter equations for supersymmetric spin chains
• TBA and Y-system for planar $Ad{S}_4/CF{T}_3$
• Exact Three-Point Functions of Determinant Operators in Planar N=4 Supersymmetric Yang-Mills Theory
• Anomalous dimensions at four loops in N=6 superconformal Chern-Simons theories
• Structure constants at wrapping order
• Exploring the mirror TBA
• Y-system and Quasi-Classical Strings
• Twist-three at five loops, Bethe Ansatz and wrapping
• Integrability of the AdS_5 x S^5 superstring and its deformations
• Baxter's Q-operators and operatorial Backlund flow for quantum (super)-spin chains
• Magnon dispersion to four loops in the ABJM and ABJ models
• Y-system, TBA and Quasi-Classical Strings in AdS4 x CP3
• The Quantum Deformed Mirror TBA I
• HHL correlators, orbit averaging and form factors
• TBA, NLO Luscher correction, and double wrapping in twisted AdS/CFT
• Wronskian Solution for AdS/CFT Y-system
• Analytic Solution of Bremsstrahlung TBA II: Turning on the Sphere Angle
• Quantum Spectral Curve for a Cusped Wilson Line in N=4 SYM
• Konishi operator at intermediate coupling
• Simplified TBA equations of the AdS_5 x S^5 mirror model
• Double Wick rotating Green-Schwarz strings
• The Bound State S-Matrix for AdS5 x S5 Superstring
• Multiple zeta functions and double wrapping in planar N=4 SYM
• Quantum Spectral Curve at Work: From Small Spin to Strong Coupling in N=4 SYM
• Classical tau-function for quantum spin chains
• PSU(2,2|4) Character of Quasiclassical AdS/CFT
• Wilson lines as superconformal defects in ABJM theory: a formula for the emitted radiation
• 5-loop Konishi from linearized TBA and the XXX magnet
• The spectral problem for strings on twisted AdS_5 x S^5
• Y-system for form factors at strong coupling in AdS5 and with multi-operator insertions in AdS3
• Quantum integrability and functional equations
• Inhomogeneous T-Q equation for the open XXX chain with general boundary terms: completeness and arbitrary spin
• Twisting the Mirror TBA
• Conformal Twists, Yang-Baxter $\sigma$-models & Holographic Noncommutativity
• Structure Constants in $\mathcal{N}=4$ SYM at Finite Coupling as Worldsheet $g$-Function
• Dimer Models and Integrable Systems
• The full Quantum Spectral Curve for $Ad{S}_4/CF{T}_3$
• Deeper Look into Short Strings
• An Integrability Primer for the Gauge-Gravity Correspondence: an Introduction
• Introduction to the thermodynamic Bethe ansatz
• Towards the exact Bremsstrahlung function of ABJM theory
• Quantum Strings and the AdS4/CFT3 Interpolating Function
• The Quantum Deformed Mirror TBA II
• Temperature quantization from the TBA equations
• Y-system and beta-deformed N=4 Super-Yang-Mills
• Monodromy Bootstrap for SU(2|2) Quantum Spectral Curves: From Hubbard model to AdS3/CFT2
• $Ad{S}_5\times S^5$ mirror TBA equations from Y-system and discontinuity relations
• Excited Hexagon Wilson Loops for Strongly Coupled N=4 SYM
• Yangians, S-matrices and AdS/CFT
• Asymptotic Bethe Ansatz on the GKP vacuum as a defect spin chain: scattering, particles and minimal area Wilson loops
• Thermodynamic Bethe Ansatz Equations for Minimal Surfaces in AdS_3
• Six-Loop Anomalous Dimension of Twist-Three Operators in N=4 SYM
• Resurgence of the Cusp Anomalous Dimension
• On classical Yang-Baxter based deformations of the AdS_5 x S^5 superstring
• On holographic three point functions for GKP strings from integrability
• Wronskian solutions of the T, Q and Y-systems related to infinite dimensional unitarizable modules of the general linear superalgebra gl(M|N)
• Infrared Stability of N=2 Chern-Simons Matter Theories
• The low-energy limit of AdS${}_3$/CFT${}_2$ and its TBA
• Surprises in the AdS algebraic curve constructions - Wilson loops and correlation functions
• Three-point Correlation functions of Giant magnons with finite size
• Three-point functions in planar N=4 super Yang-Mills Theory for scalar operators up to length five at the one-loop order
• Thermodynamic Bethe Ansatz for Fishnet CFT
• Review of AdS/CFT Integrability, Chapter III.7: Hirota Dynamics for Quantum Integrability
• The Effectiveness of Relativistic Invariance in AdS${}_3$
• Symmetries of the N=4 SYM S-matrix
• Conformal Current Algebra in Two Dimensions
• Five-loop anomalous dimension at critical wrapping order in N=4 SYM
• Quantum Spectral Curve for the eta-deformed AdS_5xS^5 superstring
• Mirror Thermodynamic Bethe Ansatz for AdS3/CFT2
• Finite-size effect for four-loop Konishi of the beta-deformed N=4 SYM
• Tree-level S-matrix of Pohlmeyer reduced form of AdS_5 x S^5 superstring theory
• Superstrings in AdS
• Holographic three-point functions for short operators
• Three-Point Functions and su(1|1) Spin Chains
• Superintegrability of Geodesic Motion on the Sausage Model
• Discrete Hirota dynamics for AdS/CFT
• General phase spaces: from discrete variables to rotor and continuum limits
• Correlation functions of magnon and spike
• The full spectrum of AdS5/CFT4 I: Representation theory and one-loop Q-system
• Yangian Symmetry and Integrability of Planar N=4 Super-Yang-Mills Theory
• Bethe Ansaetze for GKP strings
• Luescher formula for GKP string
• Hybrid-NLIE for the AdS/CFT spectral problem
• Energy-Spin Trajectories in AdS_5 x S^5 from Semiclassical Vertex Operators
• Finite Size Spectrum of SU(N) Principal Chiral Field from Discrete Hirota Dynamics
• Bound States of the q-Deformed AdS5 x S5 Superstring S-matrix
• The non-planar contribution to the four-loop universal anomalous dimension in N=4 Supersymmetric Yang-Mills theory
• Lectures on S-matrices and Integrability
• The Hagedorn temperature of AdS5/CFT4 via integrability
• String hypothesis for gl(n|m) spin chains: a particle/hole democracy
• Review of AdS/CFT Integrability, Chapter III.5: Luscher corrections
• Bound State Transfer Matrix for AdS5 x S5 Superstring
• Asymptotic Symmetries of String Theory on AdS3 X S3 with Ramond-Ramond Fluxes
• Six-loop Konishi anomalous dimension from the Y-system
• Finite-size corrections for quantum strings on AdS_4 x CP^3
• Twist operators in N=4 beta-deformed theory
• The spectrum of tachyons in AdS/CFT
• Superspace calculation of the three-loop dilatation operator of N=4 SYM theory
• The ${\mathrm{AdS}}_3\times {\mathrm{S}}^3\times {\mathrm{S}}^3\times {\mathrm{S}}^1$ worldsheet S matrix
• Three-point correlators of twist-2 operators in N=4 SYM at Born approximation
• On wrapping corrections to GKP-like operators
• Finite size corrections for open strings/open chains in planar AdS/CFT
• Six and seven loop Konishi from Luscher corrections
• Surprises from the resummation of ladders in the ABJ(M) cusp anomalous dimension
• Strong coupling results from the numerical solution of the quantum spectral curve
• Comments on the Mirror TBA
• Exploring the spectrum of planar $Ad{S}_4/CF{T}_3$ at finite coupling
• Correlation function of dyonic strings
• Resurgence of the dressing phase for ${\mathrm{AdS}}_5\times {\mathrm{S}}^5$
• On Yangian and Long Representations of the Centrally Extended su(2|2) Superalgebra
• Full Lagrangian and Hamiltonian for quantum strings on AdS_4 x CP^3 in a near plane wave limit
• Fusion of line operators in conformal sigma-models on supergroups, and the Hirota equation
• Asymptotic Four Point Functions
• QCD properties of twist operators in the N=6 Chern-Simons theory
• Quantum folded string in S^5 and the Konishi multiplet at strong coupling
• Hybrid NLIE for the Mirror AdS_5 x S^5
• Scaling dimensions from the mirror TBA
• A review of the AdS/CFT Quantum Spectral Curve
• Exceptional Operators in N=4 super Yang-Mills
• Twist-two operators and the BFKL regime - nonstandard solutions of the Baxter equation
• Quantum Spectral Curve of $\gamma$-twisted $\mathcal{N}=4$ SYM theory and fishnet CFT
• Condition on Ramond-Ramond fluxes for factorization of worldsheet scattering in anti-de Sitter space
• The Bound State S-matrix of the Deformed Hubbard Chain
• Integrability of the eta-deformed Neumann-Rosochatius model
• First-principles derivation of the AdS/CFT Y-systems
• Y-system for Y=0 brane in planar AdS/CFT
• Solving the Hagedorn temperature of AdS5/CFT4 via the Quantum Spectral Curve: Chemical potentials and deformations
• A next-to-leading Luescher formula
• Universal blocks of the AdS/CFT Scattering Matrix
• CFT data and spontaneously broken conformal invariance
• Numerical results for the exact spectrum of planar AdS4/CFT3
• Boundary finite size corrections for multiparticle states and planar AdS/CFT
• Scaling dimensions at small spin in N=4 SYM theory
• Hidden Simplicity of Gauge Theory Amplitudes
• Strings in AdS_4 x CP^3: finite size spectrum vs. Bethe Ansatz
• The non-planar contribution to the four-loop anomalous dimension of twist-2 operators: first moments in N=4 SYM and non-singlet QCD
• Structure constants of short operators in planar $\mathcal{N}=4$ SYM theory
• On the spectral problem of N=4 SYM with orthogonal or symplectic gauge group
• Finite size effect on the magnon's correlation functions
• Bethe ansatz equations for open spin chains from giant gravitons
• Six-loop anomalous dimension of twist-two operators in planar N=4 SYM theory
• Non-planar universal anomalous dimension of twist-two operators with general Lorentz spin at four loops in N=4 SYM theory
• Structure constants of heavy operators in ABJM/ABJ Theory
• Scalar Insertions in Cusped Wilson Loops in the Ladders Limit of Planar N=4 SYM
• Semiclassical folded string in AdS4 X CP3
• Integrable Wilson loops in ABJM: a $Y$-system computation of the cusp anomalous dimension
• A new representation for two- and three-point correlators of operators from sl(2) sector
• Functional Equations and Separation of Variables for Exact g-Function
• Lifting asymptotic degeneracies with the Mirror TBA
• On the Spectrum of the AdS_5xS^5 String at large lambda
• Bound States in the Mirror TBA
• Y-system for Z_S Orbifolds of N=4 SYM
• Non-planar anomalous dimension of twist-2 operators: higher moments at four loops
• On the $Ad{S}_5/CF{T}_4$ TBA and its analytic properties
• One-Loop Spectroscopy of Scalar Three-Point Functions in planar N=4 super Yang-Mills Theory
• Discontinuity relations for the AdS(4)/CFT(3) correspondence
• Twist-2 at five loops: Wrapping corrections without wrapping computations
• Reformulating the TBA equations for the quark anti-quark potential and their two loop expansion
• On string integrability. A journey through the two-dimensional hidden symmetries in the AdS/CFT dualities
• Scattering of Giant Magnons in CP^3
• Quantum Current Algebra for the $Ad{S}_5\times S^5$ Superstring
• Matching three-point functions of BMN operators at weak and strong coupling
• Chiral limit of N = 4 SYM and ABJM and integrable Feynman graphs
• ABJM quantum spectral curve and Mellin transform
• Fermions and scalars in $\mathcal{N}=4$ Wilson loops at strong coupling and beyond
• Two-Loop Spectroscopy of Short ABJM Operators
• On the logarithmic powers of $sl(2)$ SYM${}_4$
• Quasi-local formulation of the mirror TBA
• Double-logs, Gribov-Lipatov reciprocity and wrapping
• $QQ$-system and non-linear integral equations for scattering amplitudes at strong coupling
• Static Gauge and Energy Spectrum of Single-mode Strings in AdS_5xS^5
• Protected states in $\mbox{AdS}_3$ backgrounds from integrability
• Orbifolded Konishi from the Mirror TBA
• The Tetrahedron Zamolodchikov Algebra and the AdS5 x S5 S-matrix
• 6-loop anomalous dimension of a single impurity operator from AdS/CFT and multiple zeta values
• ABJM $\theta$-Bremsstrahlung at four loops and beyond
• Orbit method quantization of the AdS${}_2$ superparticle
• Yangians in Integrable Field Theories, Spin Chains and Gauge-String Dualities
• Wrapping corrections for long range spin chains
• TBA-like equations and Casimir effect in (non-)perturbative AdS/CFT
• The contribution of scalars to $\mathcal{N}=4$ SYM amplitudes II: Young tableaux, asymptotic factorisation and strong coupling
• Spin chain for the deformed ABJM theory
• SU(2|2) for Theories with Sixteen Supercharges at Weak and Strong Coupling
• Dynamic Lattice Supersymmetry in gl(n|m) Spin Chains
• Strong Wilson polygons from the lodge of free and bound mesons
• N=1 SQCD and the Transverse Field Ising Model
• Revisiting the Y=0 open spin chain at one loop
• Y-system for $\gamma$-deformed ABJM Theory
• Asymptotic Bethe equations for open boundaries in planar AdS/CFT
• N=4 SYM Quantum Spectral Curve in BFKL regime
• Giant Holes
• Generalized Gribov-Lipatov Reciprocity and AdS/CFT
• The Hirota equation for string theory in AdS5xS5 from the fusion of line operators
• Unified approach to the SU(2) Principal Chiral Field model at Finite Volume
• Semiclassical SL(2) Strings on LLM backgrounds
• Coset construction of AdS particle dynamics
• Worldsheet dilatation operator for the $AdS$ superstring
• Webs of integrable theories
• Quantum integrability of $\mathcal{N}=2$ 4d gauge theories
• Real and Virtual Bound States in Lüscher Corrections for CP3 Magnons
• The high spin expansion of twist sector dimensions: the planar N=4 super Yang-Mills theory
• Superspace methods for the computation of wrapping effects in the standard and beta-deformed N=4 SYM
• On analytical perturbative solution of ABJM quantum spectral curve
• An inhomogeneous Lax representation for the Hirota equation
• ABJM quantum spectral curve at twist 1: algorithmic perturbative solution
• The full spectrum of AdS${}_5$/CFT${}_4$ II: Weak coupling expansion via the quantum spectral curve
• Quantization of the ${\mathrm{AdS}}_3$ Superparticle on $\mathrm{OSP}(1|2{)}^2/\mathrm{SL}(2,\mathbb{R})$
• Wrapping corrections, reciprocity and BFKL beyond the sl(2) subsector in N=4 SYM
• Semiclassical energy of the $Ad{S}_4\times {\mathbb{CP}}^3$ folded string
• Integrable systems and AdS/CFT duality
• Wrapping corrections for non-diagonal boundaries in AdS/CFT
• Wrapping effects in supersymmetric gauge theories
• Exact result in N=4 SYM theory: Generalised double-logarithmic equation
• Contour deformation trick in hybrid NLIE
• On a discrete symmetry of the Bremsstrahlung function in N=4 SYM
• The complete unitary dual of non-compact Lie superalgebra su(p,q|m) via the generalised oscillator formalism, and non-compact Young diagrams
• Nonplanar Four-Loop Anomalous Dimensions of Twist-Two Operators in N=4 Super Yang-Mills Theory: Higher Moment, General Result, and Cusp Anomalous Dimension
• Extensive numerical study of a D-brane, anti-D-brane system in AdS5/CFT4
• DGLAP and BFKL equations in $\mathcal{N}=4$ SYM: from weak to strong coupling
• Comments on Correlation Functions of Large Spin Operators and Null Polygonal Wilson Loops
• Exact results for the low energy AdS(4)XCP(3) string theory
• Integrable boundaries in AdS/CFT: revisiting the Z=0 giant graviton and D7-brane
• Spectral curve for gamma-deformed AdS/CFT
• On the one-loop curvature function in the $sl(2)$ sector of $\mathcal{N}=4$ SYM
• Exact Results in Supersymmetric Gauge Theories
• Lee-Yang Model in Presence of Defects
• Operator mixing in N = 4 SYM: The Konishi anomaly re-re-visited
• Splitting strings on integrable backgrounds
• A semiclassical analysis of the fluctuation eigenvalues and the one-loop energy of the folded spinning superstring in AdS_5 x S^5
• A numerical test of the Y-system in the small size limit of the SU(2)x SU(2) Principal Chiral Model
• Beyond cusp anomalous dimension from integrability in SYM${}_4$
• Finite size effect from classical strings in $Ad{S}_3\times S^3$ with NS-NS flux
• Large spin expansion of the wrapping correction to Freyhult-Rej-Zieme twist operators
• Comments on the slope function
• A Young diagram expansion of the hexagonal Wilson loop (amplitude) in $\mathcal{N}=4$ SYM
• Canonical Description of T-duality for Fundamental String and D1-Brane and Double Wick Rotation
• A diagrammatic approach towards the thermodynamics of integrable systems
• Fermionic contribution to the anomalous dimension of twist-2 operators in N=4 SYM theory, critical indices and integrability
• On finite-size spiky strings in $Ad{S}_3\times S^3\times T^4$ with mixed fluxes
• Anomalous dimensions of twist 2 operators and $\mathcal{N}=4$ SYM quantum spectral curve