The Bethe-Ansatz for N=4 Super Yang-Mills

Abstract

We derive the one loop mixing matrix for anomalous dimensions in N=4 Super Yang-Mills. We show that this matrix can be identified with the Hamiltonian of an integrable SO(6) spin chain with vector sites. We then use the Bethe ansatz to find a recipe for computing anomalous dimensions for a wide range of operators. We give exact results for BMN operators with two impurities and results up to and including first order 1/J corrections for BMN operators with many impurities. We then use a result of Reshetikhin's to find the exact one-loop anomalous dimension for an SO(6) singlet in the limit of large bare dimension. We also show that this last anomalous dimension is proportional to the square root of the string level in the weak coupling limit.

35 pages, 3 figures, LaTeX; v2 references added, typos corrected, Λfixed; v3 expanded discussion of higher loops in conclusion, matches published version

References in corpus (10)

• Circular Semiclassical String Solutions on AdS_5 x S_5
• Operator Mixing and the BMN Correspondence
• On lightcone string field theory from Super Yang-Mills and holography
• Strings in the near plane wave background and AdS/CFT
• Tracing the String: BMN correspondence at Finite J^2/N
• Bit Strings from N=4 Gauge Theory
• Explicit Formulas for Neumann Coefficients in the Plane-Wave Geometry
• A class of exact pp-wave string models with interacting light-cone gauge actions
• On light-cone SFT contact terms in a plane wave
• On integrable models from pp-wave string backgrounds

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• Wilson loops: From four-dimensional SYM to two-dimensional YM
• A three-loop test of the dilatation operator in N=4 SYM
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• Chaos in the BMN matrix model
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• The classical R-matrix of AdS/CFT and its Lie dialgebra structure
• Comments on the beta-deformed N=4 SYM Theory
• N=4 SYM structure constants as determinants
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• Finite size giant magnons in the SU(2) x SU(2) sector of AdS_4 x CP^3
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• Proof of all-order finiteness for planar beta-deformed Yang-Mills
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• Linking Backlund and Monodromy Charges for Strings on AdS_5 x S^5
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• 1/J^2 corrections to BMN energies from the quantum long range Landau-Lifshitz model
• Exact Bremsstrahlung functions in ABJM theory
• Analytical Bethe Ansatz for closed and open gl(M|N) super-spin chains in arbitrary representations and for any Dynkin diagram
• Spin bit models from non-planar N=4 SYM
• Three-point functions in planar N=4 super Yang-Mills Theory for scalar operators up to length five at the one-loop order
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• Higher-Loop Integrability in N=4 Gauge Theory
• A new derivation of Luscher F-term and fluctuations around the giant magnon
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• The Chern-Simons Origin of Superstring Integrability
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• Analytical Bethe Ansatz for closed and open gl(n)-spin chains in any representation
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• Dilatation operator and the Super Yang-Mills duals of open strings on AdS Giant Gravitons
• Continuum limit of fishnet graphs and AdS sigma model
• Worldsheet Form Factors in AdS/CFT
• Finite-Size Effects for Multi-Magnon States
• Beyond cusp anomalous dimension from integrability
• Fluctuations and Energy Shifts in the Bethe Ansatz
• Finite-size effect for four-loop Konishi of the beta-deformed N=4 SYM
• Reflecting magnons from D7 and D5 branes
• Correlators of supersymmetric Wilson loops at weak and strong coupling
• Mirror Thermodynamic Bethe Ansatz for AdS3/CFT2
• Extended Fermion Representation of Multi-Charge 1/2-BPS Operators in AdS/CFT -- Towards Field Theory of D-Branes --
• Quantum string integrability and AdS/CFT
• Giant Magnon in NS5-brane Background
• Partial domain wall partition functions
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• Generalized Dynamical Spin Chain and 4-Loop Integrability in N=6 Superconformal Chern-Simons Theory
• Scattering in ABJ theories
• Interacting finite-size magnons
• Superstrings in AdS
• Exact S-matrices for AdS_3/CFT_2
• On the finite size corrections of anti-ferromagnetic anomalous dimensions in $\mathcal{N}=4$ SYM
• The superstring Hagedorn temperature in a pp-wave background
• Single impurity operators at critical wrapping order in the beta-deformed N=4 SYM
• Geometry and topology of bubble solutions from gauge theory
• One-Point Functions of Non-protected Operators in the SO(5) symmetric D3-D7 dCFT
• Three-Point Functions and su(1|1) Spin Chains
• From N=4 gauge theory to N=2 conformal QCD: three-loop mixing of scalar composite operators
• Conformal Dimensions of Two-Derivative BMN Operators
• The Principle of Maximal Transcendentality and the Four-Loop Collinear Anomalous Dimension
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• Nested off-diagonal Bethe ansatz and exact solutions of the su(n) spin chain with generic integrable boundaries
• Large Winding Sector of AdS/CFT
• An alternative formulation of light-cone string field theory on the plane wave
• Higher Loop Bethe Ansatz for Open Spin-Chains in AdS/CFT
• Decoupling limits of N=4 super Yang-Mills on R x S^3
• Surprises from the Resolution of Operator Mixing in N = 4 SYM
• Non-planar ABJM Theory and Integrability
• The full spectrum of AdS5/CFT4 I: Representation theory and one-loop Q-system
• Coordinate Bethe Ansatz for the String S-Matrix
• Wound and Rotating Strings in AdS_5 x S^5
• Local primordial non-Gaussianity from the large-scale clustering of photometric DESI luminous red galaxies
• q-Deformed Supersymmetry and Dynamic Magnon Representations
• Anomalous dimensions at twist-3 in the sl(2) sector of N=4 SYM
• Correlation functions of magnon and spike
• One-Loop Corrections to Type IIA String Theory in AdS4 x CP3
• Zero modes for the giant magnon
• Quantum Stability for the Heisenberg Ferromagnet
• Scattering of single spikes
• Drinfeld second realization of the quantum affine superalgebras of $D^{(1)}(2,1;x)$ via the Weyl groupoid
• An Exceptional Algebraic Origin of the AdS/CFT Yangian Symmetry
• Non-planar Anomalous Dimensions in the sl(2) Sector
• On four-point functions and integrability in N=4 SYM: from weak to strong coupling
• Spin Matrix Theory String Backgrounds and Penrose Limits of AdS/CFT
• Hubbard's Adventures in $\mathcal{N}=4$ SYM-land? Some non-perturbative considerations on finite length operators
• Correspondence between the 3-point BMN correlators and the 3-string vertex on the pp-wave
• Comments on the Boundary Scattering Phase
• Leading transcedental contribution to the four-loop universal anomalous dimension in N=4 SYM
• Higher Spins and Stringy AdS5xS5
• Beyond the Tensionless Limit: Integrability in the Symmetric Orbifold
• Quasilocality of joining/splitting strings from coherent states
• Antiferromagnetic Operators in N=4 Supersymmetric Yang-Mills Theory
• Luescher formula for GKP string
• Open Semiclassical Strings and Long Defect Operators in AdS/dCFT Correspondence
• Bubbling Orientifolds
• Note on Plane Wave Quantum Mechanics
• Multi-spin strings on AdS(5)xT(1,1) and operators of N=1 superconformal theory
• Giant Magnon on Deformed AdS(3)xS(3)
• Computing Three-Point Functions for Short Operators
• Novel construction and the monodromy relation for three-point functions at weak coupling
• Integrable Spin Chains with U(1)^3 symmetry and generalized Lunin-Maldacena backgrounds
• Lectures on S-matrices and Integrability
• One-point functions in AdS/dCFT
• Yangian symmetry of the Y=0 maximal giant graviton
• BFKL Spectrum of N=4 SYM: non-Zero Conformal Spin
• Solving and classifying the solutions of the Yang-Baxter equation through a differential approach. Two-state systems
• The non-planar contribution to the four-loop universal anomalous dimension in N=4 Supersymmetric Yang-Mills theory
• Reflecting Magnon Bound States
• N=2 Super Yang-Mills and the XXZ spin chain
• Open spin chains for giant gravitons and relativity
• Open string integrability and AdS/CFT
• The generalised scaling function: a note
• Operators, Correlators and Free Fermions for SO(N) and Sp(N)
• Dual Spikes; New Spiky String Solutions
• Open+Closed String Field Theory From Gauge Fields
• Bound State Transfer Matrix for AdS5 x S5 Superstring
• Hexagons and Correlators in the Fishnet Theory
• Matching gauge theory and string theory in a decoupling limit of AdS/CFT
• Rational $Q$-systems, Higgsing and Mirror Symmetry
• Non-planar ABJ Theory and Parity
• Diagonal Form Factors and Heavy-Heavy-Light Three-Point Functions at Weak Coupling
• Correlation Functions on the Half-BPS Wilson Loop: Perturbation and Hexagonalization
• BPS Chaos
• Spin Chain for Quantum Strings
• Spin Models and Superconformal Yang-Mills Theory
• Semiclassical strings in AdS_5 x S^5 and scalar operators in N=4 SYM theory
• A basis for large operators in N=4 SYM with orthogonal gauge group
• Notes on fast moving strings
• A two-loop test for the factorised S-matrix of planar N=4
• The generalized non-linear Schrodinger model on the interval
• Quarter BPS classified by Brauer algebra
• Asymptotic Symmetries of String Theory on AdS3 X S3 with Ramond-Ramond Fluxes
• Aspects of Non-Relativistic Quantum Field Theories
• Asymptotic Bethe Ansatz S-matrix and Landau-Lifshitz type effective 2-d actions
• Differential Cohomotopy implies intersecting brane observables via configuration spaces and chord diagrams
• The SU(2) sector in AdS/CFT
• String Bits and the Spin Vertex
• Spiky Strings and Spin Chains
• The open XXZ and associated models at q root of unity
• Factorized world-sheet scattering in near-flat AdS_5 x S^5
• Bethe Ansatz Equations for General Orbifolds of N=4 SYM
• Three-loop octagons and n-gons in maximally supersymmetric Yang-Mills theory
• Folded Three-Spin String Solutions in AdS_5 x S^5
• Landau-Lifshitz sigma-models, fermions and the AdS/CFT correspondence
• The AdS(4) x CP(3) string and its Bethe equations in the near plane wave limit
• Baxter equation for long-range SL(2|1) magnet
• The spectrum of tachyons in AdS/CFT
• Finite-size corrections for quantum strings on AdS_4 x CP^3
• Lattice Super Yang-Mills: A Virial Approach to Operator Dimensions
• Fermion BMN operators, the dilatation operator of N=4 SYM, and pp-wave string interactions
• Superspace calculation of the three-loop dilatation operator of N=4 SYM theory
• Integrability in Yang-Mills theory on the light cone beyond leading order
• On the Scattering of Magnon Boundstates
• From Free Fields to AdS -- Thermal Case
• On the Integrability of Planar N=2 Superconformal Gauge Theories
• Quantum deformed magnon kinematics
• On the Exact Interpolating Function in ABJ Theory
• Direct test of the AdS/CFT correspondence by Monte Carlo studies of N=4 super Yang-Mills theory
• On instanton contributions to anomalous dimensions in N=4 supersymmetric Yang-Mills theory
• Reconstructing 1/2 BPS Space-Time Metrics from Matrix Models and Spin Chains
• Yangian Symmetry at Two Loops for the su(2|1) Sector of N=4 SYM
• Yangian Symmetry of String Theory on $Ad{S}_3\times S^3\times S^3\times S^1$ with Mixed 3-form Flux
• OPE for Super Loops
• Light-Cone String Field Theory in a Plane Wave Background
• Spin Chains in N=2 Superconformal Theories: from the Z_2 Quiver to Superconformal QCD
• Three-point correlators from string amplitudes: Mixing and Regge spins
• On the anatomy of multi-spin magnon and single spike string solutions
• Spiky strings on AdS3 x S3 with NS-NS flux
• Effective field theory for the SO(n) bilinear-biquadratic spin chain
• Giant gravitons and the emergence of geometric limits in $\beta$-deformations of $\mathcal{N}=4$ SYM
• Precision Test of AdS/CFT in Lunin-Maldacena Background
• Singularities of the Magnon Boundstate S-Matrix
• Spin chain integrability in non-supersymmetric Wilson loops
• Generalizations of Lunin-Maldacena transformation on the $AdSsub5xSsup5$ background
• Non-compact quantum spin chains as integrable stochastic particle processes
• Slow-string limit and "antiferromagnetic" state in AdS/CFT
• Yangian Symmetry of Long-Range gl(N) Integrable Spin Chains
• 6D SCFTs, 4D SCFTs, Conformal Matter, and Spin Chains
• The Bethe Ansatz Equations for Reflecting Magnons
• Nonplanar integrability at two loops
• A note on oscillating strings in $Ad{S}_3\times S^3$ with mixed three-form fluxes
• Giant magnon bound states from strongly coupled N=4 SYM
• Giant magnons and spiky strings on the conifold
• Giant Magnons in AdS4 x CP3: Embeddings, Charges and a Hamiltonian
• Finite size corrections for open strings/open chains in planar AdS/CFT
• Open Spinning Strings and AdS/dCFT Duality
• The Leigh-Strassler Deformation and the Quest for Integrability
• Unstable Giants
• Multi-spin string solutions in AdS Black Hole and confining backgrounds
• Analytic properties of high energy production amplitudes in N=4 SUSY
• Integrability of the evolution equations for heavy-light baryon distribution amplitudes
• On two fermion BMN operators
• A supersymmetric matrix model: III. Hidden SUSY in statistical systems
• A simple collinear limit of scattering amplitudes at strong coupling
• Correlation function of dyonic strings
• A Twistorial Approach to Integrability in N=4 SYM
• Semiclassical Quantization of the Giant Magnon
• Superstring sigma models from spin chains: the SU(1,1|1) case
• What can we learn about QCD and collider physics from N=4 super Yang-Mills?
• Semiclassical Strings, Dipole Deformations of N=1 SYM and Decoupling of KK Modes
• A Quantum Check of Non-Supersymmetric AdS/dCFT
• Exploring the spectrum of planar $Ad{S}_4/CF{T}_3$ at finite coupling
• Two-loop test of the N=6 Chern-Simons theory S-matrix
• Minimal solution of the AdS/CFT crossing equation
• The generalised scaling function: a systematic study
• Sketches of emergent geometry in the gauge/gravity duality
• Neumann and Neumann-Rosochatius integrable systems from membranes on AdS_4xS^7
• Strong coupling expansion of Baxter equation in N=4 SYM
• On the propagator of a scalar field in AdS x S and in its plane wave limit
• Integrable spin chains and scattering amplitudes
• Quantum folded string in S^5 and the Konishi multiplet at strong coupling
• The S-matrix algebra of the AdS2 X S2 superstring
• Superspin chains and supersymmetric gauge theories
• Quantum Symmetries and Marginal Deformations
• On n-point Amplitudes in N=4 SYM
• A new integral representation for the scalar products of Bethe states for the XXX spin chain
• LLM Magnons
• The Complete One-Loop Dilation Operator of N=2 SuperConformal QCD
• Scattering in AdS(2)/CFT(1) and the BES Phase
• Asymptotic Four Point Functions
• Pulsating strings on $(Ad{S}_3\times S^3{)}_{\varkappa }$
• Magnetic Heisenberg-chain/pp-wave correspondence
• Exceptional Operators in N=4 super Yang-Mills
• Yangian Symmetry for the Action of Planar N=4 Super Yang-Mills and N=6 Super Chern-Simons Theories
• Quantum Spectral Curve of $\gamma$-twisted $\mathcal{N}=4$ SYM theory and fishnet CFT
• String integrability of defect CFT and dynamical reflection matrices
• BPS coherent states and localization
• Boundary Ring: a way to construct approximate NG solutions with polygon boundary conditions: I. Z_n-symmetric configurations
• A review of the AdS/CFT Quantum Spectral Curve
• Exactly solvable models in atomic and molecular physics
• Secret Symmetries in AdS/CFT
• The high energy behavior of QCD: The effective action and the triple-Pomeron-vertex
• Integrability of N=6 Chern-Simons Theory at Six Loops and Beyond
• On the commuting charges for the highest dimension SU(2) operators in planar $\mathcal{N}=4$ SYM
• Weakly coupled N=4 Super Yang-Mills and N=6 Chern-Simons theories from u(2|2) Yangian symmetry
• A Requiem for $Ad{S}_4\times \mathbb{C}{P}^3$ Fermionic self-T-duality
• Three-Point Functions of Twist-Two Operators in N=4 SYM at One Loop
• Positivity of hexagon perturbation theory
• Condition on Ramond-Ramond fluxes for factorization of worldsheet scattering in anti-de Sitter space
• Magnon-Like Dispersion Relation from M-Theory
• Integrability and Higher Loops in AdS/dCFT Correspondence
• Rotating Strings with Two Unequal Spins in Lunin-Maldacena Background
• Integrability of Smooth Wilson Loops in N=4 Superspace
• Fusion hierarchies for N = 4 superYang-Mills theory
• Universal blocks of the AdS/CFT Scattering Matrix
• Sigma model from SU(1,1|2) spin chain
• Three-point correlation functions from semiclassical circular strings
• Boundary finite size corrections for multiparticle states and planar AdS/CFT
• Duality Relations for Overlaps of Integrable Boundary States in AdS/dCFT
• Strings on conifolds from strong coupling dynamics, part I
• Open Fishchain in N=4 Supersymmetric Yang-Mills Theory
• Baecklund transformations, energy shift and the plane wave limit
• Operator Mixing and the AdS/CFT correspondence
• Circular and Folded Multi-Spin Strings in Spin Chain Sigma Models
• The su(2|3) Undynamic Spin Chain
• Divergence Cancellation and Loop Corrections in String Field Theory on a Plane Wave Background
• BPS Operators in N=4 SYM: Calogero Models and 2D Fermions
• On highest-energy state in the su(1|1) sector of N=4 super Yang-Mills theory
• Beyond the Planar Limit in ABJM
• The two-loop MHV amplitudes in N=4 supersymmetric Yang-Mills theory
• Aspects of Integrability in AdS/CFT Duality
• Magnon like solutions for strings in I-brane background
• Logarithmic Corrections to the Entanglement Entropy
• Serre Relation and Higher Grade Generators of the AdS/CFT Yangian Symmetry
• Finite-Size Corrections of the ${\mathbb{CP}}^3$ Giant Magnons: the Lüscher terms
• String bits without doubling
• Nonrelativistic Corners of $\mathcal{N}=4$ Supersymmetric Yang--Mills Theory
• Classical Integrability and Super Yangian of Superstring on AdS_5 x S^5
• Qubit Construction in 6D SCFTs
• Strings in AdS_4 x CP^3: finite size spectrum vs. Bethe Ansatz
• Integrability and non-perturbative effects in the AdS/CFT correspondence
• From finite geometry exact quantities to (elliptic) scattering amplitudes for spin chains: the 1/2-XYZ
• Hidden Simplicity of Gauge Theory Amplitudes
• TBA for non-perturbative moduli spaces
• Maximally Supersymmetric RG Flows in 4D and Integrability
• DMRG Simulation of the SU(3) AFM Heisenberg Model
• N=4 super Yang-Mills correlators without anti-commuting variables
• Anomalous dimension and local charges
• An Algebraic Setting for Defects in the XXZ and Sine-Gordon Models
• Semiclassical spectrum for BMN string in $Sc{h}_5\times S^5$
• On matrix models for anomalous dimensions of super Yang-Mills theory
• Integrability in heavy quark effective theory
• On circular strings in $(Ad{S}_3\times S^3{)}_{\varkappa }$
• Finite size effect on the magnon's correlation functions
• On the multi-spin magnon and spike solutions from membranes
• The non-planar contribution to the four-loop anomalous dimension of twist-2 operators: first moments in N=4 SYM and non-singlet QCD
• D1 and D5-brane giant gravitons on $Ad{S}_3\times S^3\times S^3\times S^1$
• Conformal Invariance in the Leigh-Strassler deformed N=4 SYM Theory
• Pulsating Strings With Angular Momenta
• On the spectral problem of N=4 SYM with orthogonal or symplectic gauge group
• Spiky strings in $\varkappa$-deformed $AdS$
• Towards a Realization of the Condensed-Matter/Gravity Correspondence in String Theory via Consistent Abelian Truncation
• Review of AdS/CFT Integrability, Chapter I.3: Long-range spin chains
• Analytical Bethe Ansatz for open spin chains with soliton non preserving boundary conditions
• 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
• Higher Loop Nonplanar Anomalous Dimensions from Symmetry
• Determinant representations for form factors in quantum integrable models with GL(3)-invariant R-matrix
• String integrability of the ABJM defect
• Instability and Degeneracy in the BMN Correspondence
• Non-planar universal anomalous dimension of twist-two operators with general Lorentz spin at four loops in N=4 SYM theory
• T-Duality of Green-Schwarz Superstrings on AdS(d) x S(d) x M(10-2d)
• Plane wave limit of local conserved charges
• Structure of the string R-matrix
• An improved AFS phase for AdS3 string integrability
• Open Perturbatively Long-Range Integrable gl(N) Spin Chains
• Bethe ansatz equations for open spin chains from giant gravitons
• Semiclassical folded string in AdS4 X CP3
• Six-loop anomalous dimension of twist-two operators in planar N=4 SYM theory
• Worldsheet scattering for the GKP string
• Operator approach to analytical evaluation of Feynman diagrams
• Integrable bootstrap for AdS3/CFT2 correlation functions
• Semi-classical Strings in Sasaki-Einstein Manifolds
• Finite size corrections and integrability of $\mathcal{N}=2$ SYM and DLCQ strings on a pp-wave
• AdS/CFT v.s. String Loops
• On the Spectrum of the AdS_5xS^5 String at large lambda
• Integrable Wilson loops in ABJM: a $Y$-system computation of the cusp anomalous dimension
• The Panorama of Spin Matrix Theory
• Functional Equations and Separation of Variables for Exact g-Function
• Integrable strings for AdS/CFT
• Where are the roots of the Bethe Ansatz equations?
• Algebraic Curve for a Cusped Wilson Line
• Quantum integrability of the Alday-Arutyunov-Frolov model
• Systematic classical continuum limits of integrable spin chains and emerging novel dualities
• Toy models for wrapping effects
• Integrable Spin Chains on the Conformal Moose
• Splitting strings and chains
• Spiky Strings and Giant Holes
• Chaotic spin chains in AdS/CFT
• On the $Ad{S}_5/CF{T}_4$ TBA and its analytic properties
• More Pendants for Polya: Two loops in the SU(2) sector
• The Anatomy of Gauge/String Duality in Lunin-Maldacena Background
• Matrix Models, Complex Geometry and Integrable Systems. I
• Kinky Strings in AdS_5 x S^5
• The Bethe Ansatz for AdS5 x S5 Bound States
• More about "short" spinning quantum strings
• Double-helix Wilson loops: case of two angular momenta
• Konishi at strong coupling from ABE
• Superstring in the plane-wave background with RR flux as a conformal field theory
• Lessons from giant gravitons on $Ad{S}_5\times T^{1,1}$
• Exciting LLM Geometries
• Introduction to the nested algebraic Bethe ansatz
• Bethe Ansatz solutions for highest states in $\mathcal{N}=4$ SYM and AdS/CFT duality
• Structure constants of operators on the Wilson loop from integrability
• Wilson-loop One-point Functions in ABJM Theory
• Finite-size corrections to the rotating string and the winding state
• Wrapping Interactions and the Konishi Operator
• N=4 Super-Yang-Mills Theory, QCD and Collider Physics
• Non-planar anomalous dimension of twist-2 operators: higher moments at four loops
• The integrable O(6) model and the correspondence: checks and predictions
• Integrability and MHV diagrams in N=4 supersymmetric Yang-Mills theory
• Issues on magnon reflection
• New aspects of the BMN correspondence beyond the planar limit
• One-Loop Spectroscopy of Scalar Three-Point Functions in planar N=4 super Yang-Mills Theory
• Spin Matrix Theory in near $\frac{1}{8}$-BPS corners of $\mathcal{N}=4$ super-Yang-Mills
• A non-integrable quench from AdS/dCFT
• Negative specific heat from non-planar interactions and small black holes in AdS/CFT
• Lambda Models From Chern-Simons Theories
• Semiclassical Strings in Electric and Magnetic Fields Deformed $Ad{S}_5\times S^5$ Spacetimes
• Integrable Subsectors from Holography
• The two-loop dilatation operator of N=4 super Yang-Mills theory in the SO(6) sector
• Nesting and Dressing
• Hints of Integrability Beyond the Planar Limit: Nontrivial Backgrounds
• On string integrability. A journey through the two-dimensional hidden symmetries in the AdS/CFT dualities
• The Morphology of N=6 Chern-Simons Theory
• On the high spin expansion in the $sl(2)$ $\mathcal{N}=4$ SYM theory
• Twist-2 at five loops: Wrapping corrections without wrapping computations
• Spiky Strings on NS5-branes
• On Three-point Functions in the AdS_4/CFT_3 Correspondence
• Integrability and unitarity
• Multi-matrix models and Noncommutative Frobenius algebras obtained from symmetric groups and Brauer algebras
• DLCQ String Spectrum from $\mathcal{N}=2$ SYM Theory
• Flavour singlets in gauge theory as Permutations
• Towards the gravity/CYBE correspondence beyond integrability -- Yang-Baxter deformations of $T^{1,1}$
• Challenges of Matrix Models
• Wilson Loop Duality and OPE for Super Form Factors of Half-BPS Operators
• Decay widths of three-impurity states in the BMN correspondence
• On the logarithmic powers of $sl(2)$ SYM${}_4$
• Exact solutions for N-magnon scattering
• $A_n^{(1)}$ affine Toda field theories with integrable boundary conditions revisited
• Giant Magnons and Spiky Strings on S^3 with B-field
• Rational Lax operators and their quantization
• ABJM quantum spectral curve and Mellin transform
• Nonlocal charges of T-dual strings
• Double-logs, Gribov-Lipatov reciprocity and wrapping
• Anomalous Dimensions of Heavy Operators from Magnon Energies
• Fermions and scalars in $\mathcal{N}=4$ Wilson loops at strong coupling and beyond
• Two-point functions of SU(2)-subsector and length-two operators in dCFT
• Introduction to Integrability and One-point Functions in $\mathcal{N}=4$ SYM and its Defect Cousin
• Non-planar cusp and transcendental anomalous dimension at four loops in N=4 supersymmetric Yang-Mills theory
• Sugawara form for AdS superstring
• Near Flat Space limit of strings on AdS_4 x CP^3
• Two-dimensional Yang-Mills theory, Painleve equations and the six-vertex model
• Protected states in $\mbox{AdS}_3$ backgrounds from integrability
• Higher point MHV amplitudes in N=4 Supersymmetric Yang-Mills Theory
• Chaining spins from (super)Yang--Mills
• Scalar fields on λ-deformed cosets
• Multiple integral formula for the off-shell six vertex scalar product
• Scattering amplitudes at strong coupling for 4K gluons
• Non-Critical Superstrings from Four-Dimensional Gauge Theory
• Trace of broken integrability in stationary correlation properties
• Correlators on the wall and ${\mathfrak{sl}}_n$ spin chain
• Relation between large dimension operators and oscillator algebra of Young diagrams
• D1-brane in beta-Deformed Background
• Spin bits at two loops
• Multispin magnons on deformed $Ad{S}_3\times S^3$
• Central Charges for the Double Coset
• On the scattering of gluons in the GKP string
• Analytical Structure of the Generalized $\lambda -$deformation
• Giant magnons and spiky strings in the Schrodinger/dipole-deformed CFT correspondence
• Magnons and BFKL
• Spiky Strings on I-brane
• Near-flat space limit and Einstein manifolds
• A note on two-spin magnon-like energy-charge relations from M-theory viewpoint
• Baxter equation beyond wrapping
• Yangian in the Twistor String
• Strings on the deformed T^{1,1}: giant magnon and single spike solutions
• New Penrose Limits and AdS/CFT
• Review of AdS/CFT Integrability, Chapter III.2: Exact world-sheet S-matrix
• Quantum fluctuations of rotating strings in AdS_5 x S^5
• Generalised T-duality and Integrable Deformations
• Cosmological Fisher forecasts for next-generation spectroscopic surveys
• A Spin Chain from String Theory
• Wrapping corrections for long range spin chains
• Lectures on Three-point Functions in N=4 Supersymmetric Yang-Mills Theory
• Algebraic Bethe ansatz for U(1) Invariant Integrable Models: Compact and non-Compact Applications
• On the singlet projector and the monodromy relation for psu(2, 2|4) spin chains and reduction to subsectors
• Reflection matrices for the $U_q[sl(m|n{)}^{(1)}]$ vertex model
• Stringy correlations on deformed $Ad{S}_3\times S^3$
• Open giant magnons on LLM geometries
• Note on Integrability of Marginally Deformed ABJ(M) Theories
• Wilson Line Correlators in N=4 Non-commutative Gauge Theory on S^2 x S^2
• Three-point functions of BMN operators at weak and strong coupling II. One loop matching
• Holography in the Large J Limit of AdS/CFT Correspondence and Its Applications
• Spin chain from membrane and the Neumann-Rosochatius integrable system
• On the origin of the dressing phase in N=4 Super Yang-Mills
• Gauge Theories as String Theories: the First Results
• Review of AdS/CFT Integrability, Chapter I.2: The spectrum from perturbative gauge theory
• Loop lessons from Wilson loops in N=4 supersymmetric Yang-Mills theory
• SU(2|2) for Theories with Sixteen Supercharges at Weak and Strong Coupling
• The Complete One-loop Spin Chain of N =1 SQCD
• TBA-like equations and Casimir effect in (non-)perturbative AdS/CFT
• Spin chain for the deformed ABJM theory
• Dynamic Lattice Supersymmetry in gl(n|m) Spin Chains
• Subleading corrections to the Double Coset Ansatz preserve integrability
• Negative anomalous dimensions in N=4 SYM
• From nesting to dressing
• Strong Wilson polygons from the lodge of free and bound mesons
• Testing the nested light-cone Bethe equations of the AdS_5 x S^5 superstring
• Refined Counting of Necklaces in One-loop $\mathcal{N}=4$ SYM
• Integrable Open Spin Chains from Flavored ABJM Theory
• The contribution of scalars to $\mathcal{N}=4$ SYM amplitudes II: Young tableaux, asymptotic factorisation and strong coupling
• BPS Condensates, Matrix Models and Emergent String Theory
• Lax pairs for string Newton Cartan geometry
• One-Loop Non-Planar Anomalous Dimensions in Super Yang-Mills Theory
• The four-point function of determinant operators in $\mathcal{N}=4$ SYM
• Octagon with finite bridge: free fermions and determinant identities
• Holographic correlators of semiclassical states in defect CFTs
• Combinatorial Solution of the Eclectic Spin Chain
• Quantum Landau-Lifshitz model at four loops: 1/J and 1/J^2 corrections to BMN energies
• Strong coupling anomalous dimensions of $\mathcal{N}=4$ super Yang-Mills
• Zero Modes for the Boundary Giant Magnons
• On the Integrability of String Theory in AdS_5 x S^5
• Exact solution and thermodynamics of a spin chain with long-range elliptic interactions
• Large-Spin Expansions of GKP Strings
• Revisiting the Y=0 open spin chain at one loop
• Large N Reductions and Holography
• Higher Charges in Dynamical Spin Chains for SYM Theory
• Asymptotic Bethe equations for open boundaries in planar AdS/CFT
• OPE in planar QCD from integrability
• On the breakdown of perturbative integrability in large N matrix models
• Chiral primaries in the Leigh-Strassler deformed N=4 SYM -- a perturbative study
• Semiclassical strings in AdS(3) X S^2
• Matrix Models, Complex Geometry and Integrable Systems. II
• Strong coupling from the Hubbard model
• SYK/AdS duality with Yang-Baxter deformations
• Statistical mechanics for dilatations in N=4 super Yang--Mills theory
• Finiteness of N =4 super-Yang-Mills effective action in terms of dressed N =1 superfields
• Large-Spin and Large-Winding Expansions of Giant Magnons and Single Spikes
• Constructing Non-Relativistic AdS${}_5$/CFT${}_4$ Holography
• Quasiclassical Geometry and Integrability of AdS/CFT Correspondence
• The dual string sigma-model of the SU_q(3) sector
• N=1 SQCD and the Transverse Field Ising Model
• Integrability and the AdS/CFT correspondence
• Yangian Symmetry in N=4 super Yang-Mills
• Is there a tower of charges to be discovered?
• N-body Dynamics of Giant Magnons in RxS2
• Analytic Bethe Ansatz and Baxter equations for long-range psl(2|2) spin chain
• Non-perturbative effects in the BMN limit of N=4 supersymmetric Yang-Mills
• Conformal higher-spin symmetries in twistor string theory
• Graph duality as an instrument of Gauge-String correspondence
• NSR String in Ads_3 Backgrounds: Nonlocal Charges
• Giant Holes
• Conformal SO(2,4) Transformations for the Helical AdS String Solution
• Field theory and $\lambda$-deformations: Expanding around the identity
• BRST Invariance of Non-local Charges and Monodromy Matrix of Bosonic String on AdS(5)xS(5)
• N=4 SYM Quantum Spectral Curve in BFKL regime
• Strings for Quantumchromodynamics
• Undular diffusion in nonlinear sigma models
• Phases of Thermal N=2 Quiver Gauge Theories
• Inelastic Magnon Scattering
• The elliptic scattering theory of the 1/2-XYZ and higher order Deformed Virasoro Algebras
• Integrability treatment of AdS/CFT orbifolds
• $C_2$ generalization of the van Diejen model from the minimal $(D_5,D_5)$ conformal matter
• Deviation from Alday-Maldacena Duality For Wavy Circle
• Multi-spike strings in $Ad{S}_3$ with mixed three-form fluxes
• Integrability and the Conformal Field Theory of the Higgs branch
• Close to the Giant Magnons
• On dilatation operator for a renormalizable theory
• On Yangian symmetry of scattering amplitudes and the dilatation operator in N=4 super Yang-Mills
• Spinning Strings on Deformed AdS_5 x T^{1,1} with NS B-field
• Perturbed symmetric-product orbifold: first-order mixing and puzzles for integrability
• Integrability of Orbifold ABJM Theories
• Perturbations of spiky strings in flat spacetimes
• New differential equations in the six-vertex model
• Semi-classical quantisation of magnetic solitons in the anisotropic Heisenberg quantum chain
• Anomalous dimensions from boson lattice models
• Semiclassical SL(2) Strings on LLM backgrounds
• The solutions of the Yang-Baxter equation for the $(n+1)(2n+1)$-vertex models through a differential approach
• Reciprocity and integrability in the sl(2) sector of N=4 SYM
• Giant Gravitons on the Schrodinger pp-wave geometry
• S-duality and the giant magnon dispersion relation
• N=(4,0) Super-Liouville Theory on the Coadjoint Orbit and PSU(1,1|2)
• A novel quasi-exactly solvable spin chain with nearest-neighbors interactions
• Correlation functions of the ABJM model
• Non-planar spin bits beyond two loops
• Perturbations of spiky strings in AdS3
• Integrable Hopf twists, marginal deformations and generalised geometry
• Elliptic String Solutions on RxS^2 and Their Pohlmeyer Reduction
• Lifting integrable models and long-range interactions
• Thermodynamics of Inozemtsev's Elliptic Spin Chain
• Giant magnons and non-maximal giant gravitons
• Probing $\eta$ deformed backgrounds with $Dp$ branes
• Strings on Plane Waves, Super-Yang Mills in Four Dimensions, Quantum Groups at Roots of One
• Marginal deformations and quasi-Hopf algebras
• Generating Functions for Giant Graviton Bound States
• QCD-like properties for anomalous dimensions in N=4 SYM
• Veneziano amplitudes, spin chains and Abelian reduction of QCD
• Superspace methods for the computation of wrapping effects in the standard and beta-deformed N=4 SYM
• Truncated Calogero-Sutherland Models on a Circle
• Heavy hadron spectra from spin chains and strings
• Bootstrability in Defect CFT: Integrated Correlators and Sharper Bounds
• On analytical perturbative solution of ABJM quantum spectral curve
• ABJM quantum spectral curve at twist 1: algorithmic perturbative solution
• Combinatorics of Wilson loops in $\mathcal{N}=4$ SYM theory
• Highest states in light-cone $Ad{S}_5\times S^5$ superstring
• Loop Operators in Three-Dimensional $\mathcal{N}=2$ Fishnet Theories
• On the Semi-Classical Limit of Scalar Products of the XXZ Spin Chain
• Intersecting Flavor Branes
• Reflection matrices with $U_q[os{p}^{(2)}(2|2m)]$ symmetry
• Bethe Ansatz for Quantum-Deformed Strings
• Exact result in N=4 SYM theory: Generalised double-logarithmic equation
• Integrability structures in string theory
• Interactions as conformal intertwiners in 4D QFT
• A perturbative approach to the non-relativistic string spectrum
• Holography of a novel codimension-2 defect CFT
• Wrapping effects in supersymmetric gauge theories
• Analytic (non)integrability of Arutyunov-Bassi-Lacroix model
• Quantum Strings and Bethe Equations
• The dilatation operator for defect conformal N=4 SYM
• Pulsating strings from two dimensional CFT on $(T^4{)}^N/S(N)$
• Boundary Giant Magnons and Giant Gravitons
• On the dynamics of BMN operators of finite size and the model of string bits
• Semiclassical Strings on Curved Branes
• Non-planar operator mixing by Brauer representations
• Microscopic formulation of the S-matrix in AdS/CFT
• Three Spin Spiky Strings in beta-deformed Background
• Dilatation operator in 3d
• D=3 N=6 superconformal symmetry of AdS_4 x CP^3 superstring
• Giant Spinons
• On the dressing phase in the SL(2) Bethe Ansatz
• Aspects of Integrability in N =4 SYM
• The Ising model and planar N=4 Yang-Mills
• Twistors, strings and supersymmetric gauge theories
• BMN operators with a scalar fermion pair and operator mixing in N=4 Super Yang-Mills Theory
• Nonplanar Four-Loop Anomalous Dimensions of Twist-Two Operators in N=4 Super Yang-Mills Theory: Higher Moment, General Result, and Cusp Anomalous Dimension
• One-point functions in $\beta$-deformed N = 4 SYM with defect
• DGLAP and BFKL equations in $\mathcal{N}=4$ SYM: from weak to strong coupling
• Kappa symmetric OSp(2|2) WZNW model
• Comments on Correlation Functions of Large Spin Operators and Null Polygonal Wilson Loops
• Multi-Spin Strings in AdS_4*CP^3 and its β-deformation
• Spinning membranes on $Ad{S}_p\times S^q$
• Neumann-Rosochatius system for (m,n) string in $Ad{S}_3\times S^3$ with mixed flux
• Consistently Constrained SL(N) WZWN Models and Classical Exchange Algebra
• Integrability of the Gauged Linear Sigma Model for AdS_5xS^5
• Exact results for the low energy AdS(4)XCP(3) string theory
• On a discrete symmetry of the Bremsstrahlung function in N=4 SYM
• The massless S-matrix of integrable $\sigma$-models
• Heavy Operators in Superconformal Chern-Simons Theory
• Scalar products and norm of Bethe vectors in ${\mathfrak{o}}_{2n+1}$ invariant integrable models
• From QCD Strings to WZW
• PSU(2,2|4) Exchange Algebra of N=4 Superconformal Multiplets
• Effects of boosting on extragalactic components: methods and statistical studies
• Neumann-Rosochatius system for strings in ABJ Model
• Spin-chain with PSU(2|2)xU(1)^3 and Non-linear Sigma-model with D(2,1;gamma)
• Singleton Strings
• Lagrangian mechanics of massless superparticle on AdS_4 x CP^3 superbackground
• Non-anomalous `Ward' identities to supplement large-N multi-matrix loop equations for correlations
• A novel class of translationally invariant spin chains with long-range interactions
• Rationality of the Anomalous Dimensions in N=4 SYM theory
• Super Yangian of superstring on AdS5xS5 revisited
• An exact solution to asymptotic Bethe equation
• A note on the Near Flat Limit for strings in the Maldacena-Nunez background
• Notes on Integrable Boundary Interactions of Open $SU(4)$ Alternating Spin Chains
• Conformal Affine Toda Soliton and Moduli of IIB Superstring on $Ad{S}_5\times S^5$
• Constraining primordial non-Gaussianity from the large scale structure two-point and three-point correlation functions
• On correlation functions in the coordinate and the algebraic Bethe ansatz
• Semiclassical Strings in Supergravity PFT
• Exact Results in Supersymmetric Gauge Theories
• Lee-Yang Model in Presence of Defects
• Spectral curve for gamma-deformed AdS/CFT
• Quantum dispersion relations for the $Ad{S}_4\times C{P}^3$ GKP string
• Perturbative Methods for Superconformal Quantum Field Theories in String - Gauge Theory Dualities
• Commuting Conformal and Dual Conformal Symmetries in the Regge limit
• Spin chains and classical strings in rotating Rindler-AdS space
• Veneziano Amplitudes, Spin Chains and String Models
• Towards deriving the AdS/CFT correspondence
• Chaotic string motion in a near pp-wave limit
• Constrained WZWN Models on G/{S x U(1)^n} and Exchange Algebra of G-Primaries
• Spinning pulsating strings in $(Ad{S}_5\times S^5{)}_{\varkappa }$
• The SU(2) Long Range Bethe Ansatz and Continuous Integrable Systems
• Interacting Emergent Yang-Mills theory
• Three-Point Functions in ABJM and Bethe Ansatz
• On Rotating and Oscillating Four-Spin Strings in AdS5 X S5
• Analytic Bethe Ansatz Solutions for Highest States in the su(1|1) and su(2) Sectors
• Reflection $K$-matrices for a nineteen vertex model with $U_q[\mathrm{osp}{\left(2|2\right)}^{\left(2\right)}]$ symmetry
• Algebra of Lax Connection for T-Dual Models
• Yangian Symmetry, S-Matrices and Bethe Ansatz for the AdS5 x S5 Superstring
• The Hagedorn temperature in a decoupled sector of AdS/CFT
• Bound State Scattering Simplified
• Perturbative 4D conformal field theories and representation theory of diagram algebras
• Supergraphs and the cubic Leigh-Strassler model
• Gauge-String Dualities and Some Applications
• Fermion zero modes for the mixed-flux AdS${}_3$ giant magnon
• Conformal Mapping of Non-Lorentzian Geometries in SU(1,2) Conformal Field Theory
• Hawking-Page transition on a spin chain
• The Omega-Infinity Limit of Single Spikes
• The QCD spin chain S matrix
• 12 loops and triple wrapping in ABJM theory from integrability
• The SU(1|2) and SU(2|2) Sectors from Superstrings in AdS5 x S5
• Integrability and scattering of the boson field theory on a lattice
• Finite-size Effect for Dyonic Giant Magnons in $C{P}_{\beta }^3$
• On emergence in gauge theories at the 't Hooft limit
• Finite size effect from classical strings in $Ad{S}_3\times S^3$ with NS-NS flux
• World-Sheets from N=4 Super Yang-Mills
• Integrability and Conformal Blocks for Surface Defects in $\mathcal{N}=4$ SYM
• Spiky Strings with Two Spins in AdS5
• Finite Size Effect from Classical Strings in deformed AdS${}_3\times$ S${}^3$
• Aspects of Supersymmetric Gauge Theory and String Theory
• Large-Spin Expansions of Giant Magnons
• BPS Monopoles and Open Spin Chains
• Multi-trace Correlators from Permutations as Moduli Space
• Rotating and Orbiting Strings in Dp-brane background
• Semiclassical quantization of the mixed-flux AdS${}_3$ giant magnon
• Neumann-Rosochatius system for strings on I-brane
• Large N anomalous dimensions for large operators in Leigh-Strassler deformed SYM
• Strings, Integrable Systems, Geometry and Statistical Models
• Renormalization group flow of reduced string actions
• Integrability and Matrix Models
• Gluon scattering amplitudes from gauge/string duality and integrability
• On string solutions of Bethe equations in N=4 supersymmetric Yang-Mills theory
• A Young diagram expansion of the hexagonal Wilson loop (amplitude) in $\mathcal{N}=4$ SYM
• Quantum integrable systems. Quantitative methods in biology
• A hitchhiker's guide to quantum field theoretic aspects of $\mathcal{N}=4$ SYM theory and its deformations
• On-shell Methods for Form Factors in N=4 SYM and Their Applications
• Gravitational realization of magnons in a ferromagnetic spin chain
• Spin-$s$ $Q$-systems: Twist and Open Boundaries
• A boundary matrix for AdS/CFT SU(1|1) spin chain
• Boundary Algebraic Bethe Ansatz for a nineteen vertex model with $U_q[\mathrm{osp}(2|2{)}^{(2)}]$ symmetry
• Dynamical supersymmetry on the XXX spin chain
• Splitting of Folded Strings in AdS_4*CP^3
• Integrable models: from dynamical solutions to string theory
• D-branes, gauge/string duality and noncommutative theories
• Large-N Limit as a Classical Limit: Baryon in Two-Dimensional QCD and Multi-Matrix Models
• Neumann-Rosochatius system for rotating strings in $Ad{S}_3\times S^3\times S^3\times S^1$ with flux
• A short review on TBA equation and scattering amplitude/Wilson loop duality
• On the Integrable Structure of Super Yang-Mills Scattering Amplitudes
• The spectral curve of segmented strings
• Perturbations of giant magnons and single spikes in $\mathbb{R}\times S^2$
• Superstring in the pp-wave background with RR flux as a conformal field theory
• On the algebraic curves for circular and folded strings in ${\text{AdS}}_5\times S^5$
• Deforming integrable models of AdS${}_3$ strings
• On finite-size spiky strings in $Ad{S}_3\times S^3\times T^4$ with mixed fluxes