The su(2|2) Dynamic S-Matrix

Abstract

We derive and investigate the S-matrix for the su(2|3) dynamic spin chain and for planar N=4 super Yang-Mills. Due to the large amount of residual symmetry in the excitation picture, the S-matrix turns out to be fully constrained up to an overall phase. We carry on by diagonalising it and obtain Bethe equations for periodic states. This proves an earlier proposal for the asymptotic Bethe equations for the su(2|3) dynamic spin chain and for N=4 SYM.

29 pages. v2: references added, minor corrections. v3: form of terms in table 1 improved, minor corrections, v4: missed to correct (D.3) in v3, footnote and reference added

Cited by in corpus (326)

• Foundations of the AdS_5 x S^5 Superstring. Part I
• Integrability for the Full Spectrum of Planar AdS/CFT II
• Integrability for the Full Spectrum of Planar AdS/CFT
• Thermodynamic Bethe Ansatz for the AdS_5 x S^5 Mirror Model
• Integrability and the AdS(3)/CFT(2) correspondence
• The quark anti-quark potential and the cusp anomalous dimension from a TBA equation
• Exact AdS/CFT spectrum: Konishi dimension at any coupling
• Non-Relativistic Strings and Limits of the AdS/CFT Correspondence
• Spin Chains in N=6 Superconformal Chern-Simons-Matter Theory
• String hypothesis for the AdS_5 x S^5 mirror
• Quantum spectral curve for arbitrary state/operator in AdS${}_5$/CFT${}_4$
• Thermodynamic Bethe Ansatz for planar AdS/CFT: a proposal
• Hexagonalization of Correlation Functions
• On three-point correlation functions in the gauge/gravity duality
• Strings with Non-Relativistic Conformal Symmetry and Limits of the AdS/CFT Correspondence
• Strings on NS-NS Backgrounds as Integrable Deformations
• Space-time S-matrix and Flux-tube S-matrix III. The two-particle contributions
• One-loop four-point amplitudes in pure and matter-coupled N <= 4 supergravity
• 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
• Five loop Konishi from AdS/CFT
• Integrable Wilson loops
• A dynamic su(1|1)^2 S-matrix for AdS3/CFT2
• Tessellating cushions: four-point functions in N=4 SYM
• 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
• Towards a two-parameter q-deformation of AdS_3 x S^3 x M^4 superstrings
• On correlation functions of operators dual to classical spinning string states
• Integrability, spin-chains and the AdS3/CFT2 correspondence
• All-loop Bethe ansatz equations for AdS3/CFT2
• Classical integrability and quantum aspects of the AdS(3) x S(3) x S(3) x S(1) superstring
• Dressing phases of AdS3/CFT2
• Long-Range Deformations for Integrable Spin Chains
• Five-loop Konishi from the Mirror TBA
• Massive S-matrix of AdS_3 x S^3 x T^4 superstring theory with mixed 3-form flux
• Towards integrability for AdS3/CFT2
• Scattering in Mass-Deformed N>=4 Chern-Simons Models
• Massive N=2 Gauge Theories at Large N
• q-Deformation of the AdS5 x S5 Superstring S-matrix and its Relativistic Limit
• Quantum spectral curve as a tool for a perturbative quantum field theory
• The Dressing Factor and Crossing Equations
• Correlation functions of three heavy operators - the AdS contribution
• Near BMN dynamics of the AdS(3) x S(3) x S(3) x S(1) superstring
• Worldsheet scattering in AdS(3)/CFT(2)
• TBA and Y-system for planar $Ad{S}_4/CF{T}_3$
• Worldsheet spectrum in AdS(4)/CFT(3) correspondence
• Exact Three-Point Functions of Determinant Operators in Planar N=4 Supersymmetric Yang-Mills Theory
• 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
• Integrable spin chain for stringy Wess-Zumino-Witten models
• Perturbative Four-Point Functions In Planar N=4 SYM From Hexagonalization
• Lectures on the Bethe Ansatz
• Twist-three at five loops, Bethe Ansatz and wrapping
• Non-perturbative Defect One-Point Functions in Planar $\mathcal{N}=4$ Super-Yang-Mills
• Y-system and Quasi-Classical Strings
• Integrability of the AdS_5 x S^5 superstring and its deformations
• The generalized cusp in ABJ(M) N = 6 Super Chern-Simons theories
• Colour-dressed hexagon tessellations for correlation functions and non-planar corrections
• Comment on the Scaling Function in AdS4 x CP3
• Y-system, TBA and Quasi-Classical Strings in AdS4 x CP3
• The Quantum Deformed Mirror TBA I
• Wronskian Solution for AdS/CFT Y-system
• HHL correlators, orbit averaging and form factors
• Konishi operator at intermediate coupling
• Two-dimensional S-matrices from unitarity cuts
• Spin Matrix Theory: A quantum mechanical model of the AdS/CFT correspondence
• The Bound State S-Matrix for AdS5 x S5 Superstring
• Three-point functions in $\mathcal{N}=4$ SYM: the hexagon proposal at three loops
• PSU(2,2|4) Character of Quasiclassical AdS/CFT
• Spin Chain Overlaps and the Twisted Yangian
• The classical R-matrix of AdS/CFT and its Lie dialgebra structure
• N=4 SYM structure constants as determinants
• Structure Constants in $\mathcal{N}=4$ SYM at Finite Coupling as Worldsheet $g$-Function
• Twisting the Mirror TBA
• Hexagonalization of Correlation Functions II: Two-Particle Contributions
• An Integrability Primer for the Gauge-Gravity Correspondence: an Introduction
• Deeper Look into Short Strings
• Giant gravitons: a collective coordinate approach
• Temperature quantization from the TBA equations
• Quantum deformations of the flat space superstring
• On the Dressing Factors, Bethe Equations and Yangian Symmetry of Strings on AdS3 x S3 x T4
• The Classical Exchange Algebra of AdS5 x S5 String Theory
• Monodromy Bootstrap for SU(2|2) Quantum Spectral Curves: From Hubbard model to AdS3/CFT2
• Finite Size Giant Magnon
• $T\bar{T}$ deformations as TsT transformations
• Review of AdS/CFT Integrability, Chapter III.3: The dressing factor
• Twisted Bethe equations from a twisted S-matrix
• A light-cone approach to three-point functions in AdS_5 x S^5
• $Ad{S}_5\times S^5$ mirror TBA equations from Y-system and discontinuity relations
• Yangians, S-matrices and AdS/CFT
• Six-Loop Anomalous Dimension of Twist-Three Operators in N=4 SYM
• Yang-Baxter and the Boost: splitting the difference
• Integrable S-matrices, massive and massless modes and the AdS_2 x S^2 superstring
• Secret Symmetries of Type IIB Superstring Theory on AdS3 x S3 x M4
• Integrability in N=2 superconformal gauge theories
• Handling Handles. Part II. Stratification and Data Analysis
• Three-point correlators for giant magnons
• Restoring Unitarity in the q-Deformed World-Sheet S-Matrix
• Thermodynamic Bethe Ansatz for Fishnet CFT
• The virtual scaling function of AdS/CFT
• Bonus Yangian Symmetry for the Planar S-Matrix of N=4 Super Yang-Mills
• Three-point functions in planar N=4 super Yang-Mills Theory for scalar operators up to length five at the one-loop order
• UV finiteness of Pohlmeyer-reduced form of the AdS_5xS^5 superstring theory
• The Classical Trigonometric r-Matrix for the Quantum-Deformed Hubbard Chain
• Worldsheet Form Factors in AdS/CFT
• The AdS(5)xS(5) Semi-Symmetric Space Sine-Gordon Theory
• Finite-size effect for four-loop Konishi of the beta-deformed N=4 SYM
• Mirror Thermodynamic Bethe Ansatz for AdS3/CFT2
• Tree-level S-matrix of Pohlmeyer reduced form of AdS_5 x S^5 superstring theory
• Generalized Dynamical Spin Chain and 4-Loop Integrability in N=6 Superconformal Chern-Simons Theory
• A Relativistic Relative of the Magnon S-Matrix
• Correlation functions of magnon and spike
• Spin Matrix Theory String Backgrounds and Penrose Limits of AdS/CFT
• Non-split and split deformations of AdS_5
• Beyond the Tensionless Limit: Integrability in the Symmetric Orbifold
• Energy-Spin Trajectories in AdS_5 x S^5 from Semiclassical Vertex Operators
• Yangian symmetry and bound states in AdS/CFT boundary scattering
• Yangian symmetry of the Y=0 maximal giant graviton
• Open spin chains for giant gravitons and relativity
• Lectures on S-matrices and Integrability
• Matching gauge theory and string theory in a decoupling limit of AdS/CFT
• Bound State Transfer Matrix for AdS5 x S5 Superstring
• Yangian of AdS3/CFT2 and its deformation
• Aspects of Non-Relativistic Quantum Field Theories
• Finite-size corrections for quantum strings on AdS_4 x CP^3
• On the Integrability of Planar N=2 Superconformal Gauge Theories
• Superspace calculation of the three-loop dilatation operator of N=4 SYM theory
• Operator mixing and three-point functions in 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
• The RTT-Realization for the Deformed gl(2|2) Yangian
• The Bethe Ansatz Equations for Reflecting Magnons
• Giant gravitons and the emergence of geometric limits in $\beta$-deformations of $\mathcal{N}=4$ SYM
• Giant Magnons in AdS4 x CP3: Embeddings, Charges and a Hamiltonian
• Finite size corrections for open strings/open chains in planar AdS/CFT
• Comments on the Mirror TBA
• A note on oscillating strings in $Ad{S}_3\times S^3$ with mixed three-form fluxes
• Diagonal form factors and hexagon form factors
• Giant magnons and spiky strings on the conifold
• On Yangian and Long Representations of the Centrally Extended su(2|2) Superalgebra
• Two-loop test of the N=6 Chern-Simons theory S-matrix
• Integrable open spin-chains in AdS3/CFT2 correspondences
• Minimal solution of the AdS/CFT crossing equation
• Scattering in AdS(2)/CFT(1) and the BES Phase
• Giant Magnons on CP^3 by Dressing Method
• Finite-size Effect of the Dyonic Giant Magnons in N=6 super Chern-Simons Theory
• Quantum Symmetries and Marginal Deformations
• The Complete One-Loop Dilation Operator of N=2 SuperConformal QCD
• LLM Magnons
• The S-matrix algebra of the AdS2 X S2 superstring
• Pulsating strings on $(Ad{S}_3\times S^3{)}_{\varkappa }$
• Classical and quantum integrability in AdS(2)/CFT(1)
• Massless S matrices for AdS3/CFT2
• Secret Symmetries in AdS/CFT
• Achiral boundaries and the twisted Yangian of the D5-brane
• Positivity of hexagon perturbation theory
• The Bound State S-matrix of the Deformed Hubbard Chain
• Y-system for Y=0 brane in planar AdS/CFT
• Weakly coupled N=4 Super Yang-Mills and N=6 Chern-Simons theories from u(2|2) Yangian symmetry
• Integrability of N=6 Chern-Simons Theory at Six Loops and Beyond
• A next-to-leading Luescher formula
• Three-point correlation functions from semiclassical circular strings
• Boundary finite size corrections for multiparticle states and planar AdS/CFT
• Universal blocks of the AdS/CFT Scattering Matrix
• Wrapping in maximally supersymmetric and marginally deformed N=4 Yang-Mills
• Lie Algebra Expansion and Integrability in Superstring Sigma-Models
• 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
• Strings in AdS_4 x CP^3: finite size spectrum vs. Bethe Ansatz
• Integrable achiral D5-brane reflections and asymptotic Bethe equations
• Classifying integrable symmetric space strings via factorized scattering
• On circular strings in $(Ad{S}_3\times S^3{)}_{\varkappa }$
• A Topologically Massive Gauge Theory with 32 Supercharges
• Fermionic Correlators from Integrability
• Pulsating Strings With Angular Momenta
• Review of AdS/CFT Integrability, Chapter I.3: Long-range spin chains
• On the spectral problem of N=4 SYM with orthogonal or symplectic gauge group
• Finite size effect on the magnon's correlation functions
• Review of AdS/CFT Integrability, Chapter II.2: Quantum Strings in AdS5xS5
• Maximally Supersymmetric RG Flows in 4D and Integrability
• Maximally extended sl(2|2), q-deformed d(2,1;epsilon) and 3D kappa-Poincaré
• Yangian symmetry of boundary scattering in AdS/CFT and the explicit form of bound state reflection matrices
• Bethe ansatz for an AdS/CFT open spin chain with non-diagonal boundaries
• Structure of the string R-matrix
• Separation of variables bases for integrable $g{l}_{\mathcal{M}|\mathcal{N}}$ and Hubbard models
• Integrable Wilson loops in ABJM: a $Y$-system computation of the cusp anomalous dimension
• Integrable bootstrap for AdS3/CFT2 correlation functions
• On the worldsheet theory of the type IIA AdS(4) x CP(3) superstring
• On the pulsating strings in AdS_5 x T^{1,1}
• Exciting LLM Geometries
• Wilson-loop One-point Functions in ABJM Theory
• Structure constants of operators on the Wilson loop from integrability
• Spiky Strings and Giant Holes
• Hubbard-Shastry lattice models
• The Semi-Classical Spectrum of Solitons and Giant Magnons
• The Relativistic Avatars of Giant Magnons and their S-Matrix
• On the reflection of magnon bound states
• The Bethe Ansatz for AdS5 x S5 Bound States
• One-Dimensional Sectors From the Squashed Three-Sphere
• Twist-2 at five loops: Wrapping corrections without wrapping computations
• Massless $Ad{S}_2$ scattering and Bethe ansatz
• On string integrability. A journey through the two-dimensional hidden symmetries in the AdS/CFT dualities
• Quantum finite-size effects for dyonic magnons in the AdS_4 x CP^3
• An alternative S-matrix for N=6 Chern-Simons theory ?
• Integrable Subsectors from Holography
• Hints of Integrability Beyond the Planar Limit: Nontrivial Backgrounds
• Coherent state operators, giant gravitons, and gauge-gravity correspondence
• The Tensionless Limit of Pure-Ramond-Ramond AdS3/CFT2
• ABJM quantum spectral curve and Mellin transform
• Strings on Bubbling Geometries
• Representations of centrally extended Lie superalgebra $\mathfrak{psl}(2|2)$
• Anomalous Dimensions of Heavy Operators from Magnon Energies
• N=4 Supersymmetric Landau Models
• On the pulsating strings in AdS_4 x CP3
• Maximally extended sl(2|2) as a quantum double
• Coherent state excitations and string-added coherent states in gauge-gravity correspondence
• Scattering of Giant Magnons in CP^3
• Double-logs, Gribov-Lipatov reciprocity and wrapping
• Giant magnons and spiky strings in the Schrodinger/dipole-deformed CFT correspondence
• Extremal chiral ring states in AdS/CFT are described by free fermions for a generalized oscillator algebra
• Central Charges for the Double Coset
• Dynamical Spin Chains in 4D $\mathcal{N}=2$ SCFTs
• $q$-Poincaré supersymmetry in $Ad{S}_5/CF{T}_4$
• The Tetrahedron Zamolodchikov Algebra and the AdS5 x S5 S-matrix
• Spiky Strings on I-brane
• Multispin magnons on deformed $Ad{S}_3\times S^3$
• New Penrose Limits and AdS/CFT
• Note on Integrability of Marginally Deformed ABJ(M) Theories
• Strings on the deformed T^{1,1}: giant magnon and single spike solutions
• Giant Magnons of String Theory in the Lambda Background
• Fusion for the one-dimensional Hubbard model
• Nonlocal Symmetries and Factorized Scattering
• Open giant magnons on LLM geometries
• All Jordanian deformations of the $Ad{S}_5\times S^5$ superstring
• Emergent Yang-Mills theory
• Stringy correlations on deformed $Ad{S}_3\times S^3$
• Review of AdS/CFT Integrability, Chapter III.2: Exact world-sheet S-matrix
• Note on Centrally Extended su(2/2) and Serre Relations
• Off-shell symmetry algebra of the AdS_4 x CP^3 superstring
• Spin chain for the deformed ABJM theory
• Finite-size effects of beta-deformed AdS_5/CFT_4 at strong coupling
• The Complete One-loop Spin Chain of N =1 SQCD
• Zero Modes for the Boundary Giant Magnons
• Review of AdS/CFT Integrability, Chapter I.2: The spectrum from perturbative gauge theory
• SU(2|2) for Theories with Sixteen Supercharges at Weak and Strong Coupling
• Giant Magnons in Symmetric Spaces: Explicit N-soliton solutions for CP^n, SU(n) and S^n
• Three-point functions at strong coupling in the BMN limit
• Multispin magnons from Spin-Matrix strings on $Ad{S}_5\times S^5$
• Nonrelativistic giant magnons from Newton Cartan strings
• S matrix for a three-parameter integrable deformation of $Ad{S}_3\times S^3$ strings
• Large-Spin and Large-Winding Expansions of Giant Magnons and Single Spikes
• Large-Spin Expansions of GKP Strings
• Asymptotic Bethe equations for open boundaries in planar AdS/CFT
• The secret symmetries of the AdS/CFT reflection matrices
• On the absence of reflection in AdS4/CFT3
• $q$-Poincaré invariance of the $Ad{S}_3/CF{T}_2$ $R$-matrix
• N=1 SQCD and the Transverse Field Ising Model
• An algebraic approach to the Hubbard model
• The Yangian of sl(n|m) and the universal R-matrix
• Contracted and expanded integrable structures
• Giant Holes
• Inelastic Magnon Scattering
• Semiclassical SL(2) Strings on LLM backgrounds
• On $Ad{S}_2/CF{T}_1$ transfer matrices, Bethe ansatz and scale invariance
• The splitting of electrons and violation of the Luttinger sum rule
• Reflection algebra, Yangian symmetry and bound-states in AdS/CFT
• N=(4,0) Super-Liouville Theory on the Coadjoint Orbit and PSU(1,1|2)
• String junctions suspended between giants
• Anomalous dimensions from boson lattice models
• Perturbed symmetric-product orbifold: first-order mixing and puzzles for integrability
• S-duality and the giant magnon dispersion relation
• Spinning Hexagons
• Real and Virtual Bound States in Lüscher Corrections for CP3 Magnons
• Four-loop anomalous dimensions in Leigh-Strassler deformations
• D5-brane boundary reflection factors
• Giant magnons and non-maximal giant gravitons
• Wrapping effects in supersymmetric gauge theories
• Boundary Giant Magnons and Giant Gravitons
• The Quantum Affine Origin of the AdS/CFT Secret Symmetry
• Wrapping corrections for non-diagonal boundaries in AdS/CFT
• Interacting Double Coset Magnons
• Oscillating Multiple Giants
• Bethe Ansatz for Quantum-Deformed Strings
• D=3 N=6 superconformal symmetry of AdS_4 x CP^3 superstring
• On analytical perturbative solution of ABJM quantum spectral curve
• ABJM quantum spectral curve at twist 1: algorithmic perturbative solution
• Giant Spinons
• Semiclassical Strings on Curved Branes
• Matrix Reduction and the su(2|2) superalgebra in AdS/CFT
• Classical Lie Bialgebras for AdS/CFT Integrability by Contraction and Reduction
• Integrability of the Gauged Linear Sigma Model for AdS_5xS^5
• Drinfeld realization of the centrally extended $\mathfrak{psl}(2|2)$ Yangian algebra with the manifest coproducts
• BMN operators with a scalar fermion pair and operator mixing in N=4 Super Yang-Mills Theory
• Entanglement Entropy of the N=4 SYM spin chain
• A Supersymmetry Preserving Mass-Deformation of N=1 Super Yang-Mills in D=2+1
• Rotating Restricted Schur Polynomials
• New R-matrices with non-additive spectral parameters and integrable models of strongly correlated fermions
• Integrable boundaries in AdS/CFT: revisiting the Z=0 giant graviton and D7-brane
• Spin-chain with PSU(2|2)xU(1)^3 and Non-linear Sigma-model with D(2,1;gamma)
• Geometry of Massless Scattering in Integrable Superstring
• Spectral curve for gamma-deformed AdS/CFT
• Constrained WZWN Models on G/{S x U(1)^n} and Exchange Algebra of G-Primaries
• Killing scalar of non-linear sigma models on G/H realizing the classical exchange algebra
• Super Landau Models on Odd Cosets
• Fermion zero modes for the mixed-flux AdS${}_3$ giant magnon
• Four-Point Functions with a Twist
• Fusion for AdS/CFT boundary S-matrices
• Interacting Emergent Yang-Mills theory
• Algebraic Geometry methods associated to the one-dimensional Hubbard model
• A note on open-chain transfer matrices from q-deformed su(2|2) S-matrices
• Complex D($2,1;\zeta$) and spin chain solutions from Chern-Simons theory
• Yangian Symmetry, S-Matrices and Bethe Ansatz for the AdS5 x S5 Superstring
• Bound State Scattering Simplified
• Twisted Yangian symmetry of the open Hubbard model
• On matrix realizations of the Lie superalgebra D(2, 1 ; α)
• The Omega-Infinity Limit of Single Spikes
• A study of integrable form factors in massless relativistic $Ad{S}_2$
• Semiclassical quantization of the mixed-flux AdS${}_3$ giant magnon
• An Algebraic Model for the su(2|2) Light-Cone String Field Theory
• Quantum Spectral Curve for AdS${}_3$/CFT${}_2$: a proposal
• On non-canonical degrees of freedom
• A boundary matrix for AdS/CFT SU(1|1) spin chain
• Transfer matrices for AdS3/CFT2
• Boundary bound states and integrable Wilson loops in ABJM
• Worldsheet one-loop energy correction to IIA Giant Magnon