On the Hopf algebra structure of the AdS/CFT S-matrix

Abstract

We formulate the Hopf algebra underlying the su(2|2) worldsheet S-matrix of the AdS_5 x S^5 string in the AdS/CFT correspondence. For this we extend the previous construction in the su(1|2) subsector due to Janik to the full algebra by specifying the action of the coproduct and the antipode on the remaining generators. The nontriviality of the coproduct is determined by length-changing effects and results in an unusual central braiding. As an application we explicitly determine the antiparticle representation by means of the established antipode.

12 pages, no figures, minor changes, typos corrected, comments and references added, v3: three references added

References in corpus (36)

• The Bethe-Ansatz for N=4 Super Yang-Mills
• Hidden Symmetries of the AdS_5 x S^5 Superstring
• The N=4 SYM Integrable Super Spin Chain
• The Dilatation Operator of Conformal N=4 Super Yang-Mills Theory
• Long-Range PSU(2,2|4) Bethe Ansaetze for Gauge Theory and Strings
• Bethe Ansatz for Quantum Strings
• The Complete One-Loop Dilatation Operator of N=4 Super Yang-Mills Theory
• Classical/quantum integrability in AdS/CFT
• A Novel Long Range Spin Chain and Planar N=4 Super Yang-Mills
• Multi-spin string solutions in AdS_5 x S^5
• The Factorized S-Matrix of CFT/AdS
• The AdS_5xS^5 superstring worldsheet S-matrix and crossing symmetry
• The Dilatation Operator of N=4 Super Yang-Mills Theory and Integrability
• The su(2|3) Dynamic Spin Chain
• Spinning strings in AdS_5 x S^5 and integrable systems
• Spinning strings in AdS_5 x S^5: new integrable system relations
• Quantum corrections to the string Bethe ansatz
• Planar N=4 gauge theory and the Inozemtsev long range spin chain
• Quantizing String Theory in AdS_5 X S^5: Beyond the pp-Wave
• Integrable Hamiltonian for Classical Strings on AdS_5 x S^5
• Spinning strings and AdS/CFT duality
• On AdS_5 x S^5 String S-matrix
• On Quantum Corrections to Spinning Strings and Bethe Equations
• Holography Beyond the Penrose Limit
• On Integrability of Classical SuperStrings in AdS_5 x S^5
• The AdS5xS5 Superstring in Light-Cone Gauge and its Bethe Equations
• Quantum corrections to spinning strings in AdS(5)xS(5) and Bethe ansatz: a comparative study
• A Universality Test of the Quantum String Bethe Ansatz
• Higher Impurity AdS/CFT Correspondence in the Near-BMN Limit
• Stringy sums and corrections to the quantum string Bethe ansatz
• Bethe Ansatz in Stringy Sigma Models
• Solutions to the Quantum Yang-Baxter Equation with Extra Non-Additive Parameters
• On the Construction of Trigonometric Solutions of the Yang-Baxter Equation
• Long-Range GL(n) Integrable Spin Chains and Plane-Wave Matrix Theory
• On the Scattering Phase for AdS_5 x S^5 Strings
• Exact S-Matrices with Affine Quantum Group Symmetry

Cited by in corpus (87)

• Foundations of the AdS_5 x S^5 Superstring. Part I
• A Crossing-Symmetric Phase for AdS_5 x S^5 Strings
• The Zamolodchikov-Faddeev Algebra for AdS_5 x S^5 Superstring
• On String S-matrix, Bound States and TBA
• The Analytic Bethe Ansatz for a Chain with Centrally Extended su(2|2) Symmetry
• The Off-shell Symmetry Algebra of the Light-cone AdS_5 x S^5 Superstring
• Quantum Deformations of the One-Dimensional Hubbard Model
• The complete worldsheet S matrix of superstrings on AdS_3 x S^3 x T^4 with mixed three-form flux
• Worldsheet Scattering in AdS_5 x S^5
• 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
• The complete AdS_3 x S^3 x T^4 worldsheet S-matrix
• Towards a two-parameter q-deformation of AdS_3 x S^3 x M^4 superstrings
• Connecting giant magnons to the pp-wave: An interpolating limit of $Ad{S}_5\times S^5$
• Massive S-matrix of AdS_3 x S^3 x T^4 superstring theory with mixed 3-form flux
• Towards integrability for AdS3/CFT2
• The Classical r-matrix of AdS/CFT and its Lie Bialgebra Structure
• S-matrix for magnons in the D1-D5 system
• The Bound State S-Matrix for AdS5 x S5 Superstring
• On Drinfeld's second realization of the AdS/CFT su(2|2) Yangian
• The classical R-matrix of AdS/CFT and its Lie dialgebra structure
• Quantum integrability and functional equations
• Classical r-matrix of the su(2|2) SYM spin-chain
• A Secret Symmetry of the AdS/CFT S-matrix
• Yangians, S-matrices and AdS/CFT
• A Quantum Affine Algebra for the Deformed Hubbard Chain
• A Yangian Double for the AdS/CFT Classical r-matrix
• Secret Symmetries of Type IIB Superstring Theory on AdS3 x S3 x M4
• Integrable S-matrices, massive and massless modes and the AdS_2 x S^2 superstring
• On Symmetry Enhancement in the psu(1,1|2) Sector of N=4 SYM
• The Classical Trigonometric r-Matrix for the Quantum-Deformed Hubbard Chain
• q-Deformed Supersymmetry and Dynamic Magnon Representations
• 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
• Yangian of AdS3/CFT2 and its deformation
• Reciprocity of gauge operators in N=4 SYM
• Landau-Lifshitz sigma-models, fermions and the AdS/CFT correspondence
• Quantum deformed magnon kinematics
• The RTT-Realization for the Deformed gl(2|2) Yangian
• Semiclassical Quantization of the Giant Magnon
• Integrable open spin-chains in AdS3/CFT2 correspondences
• On Yangian and Long Representations of the Centrally Extended su(2|2) Superalgebra
• The S-matrix algebra of the AdS2 X S2 superstring
• Free Fermions, vertex Hamiltonians, and lower-dimensional AdS/CFT
• Weakly coupled N=4 Super Yang-Mills and N=6 Chern-Simons theories from u(2|2) Yangian symmetry
• Secret Symmetries in AdS/CFT
• The su(2|3) Undynamic Spin Chain
• Universal blocks of the AdS/CFT Scattering Matrix
• Physical Constraints on Quantum Deformations of Spacetime Symmetries
• Serre Relation and Higher Grade Generators of the AdS/CFT Yangian Symmetry
• Maximally extended sl(2|2), q-deformed d(2,1;epsilon) and 3D kappa-Poincaré
• Structure of the string R-matrix
• Review of AdS/CFT Integrability, Chapter III.4: Twist states and the cusp anomalous dimension
• The Bethe Ansatz for AdS5 x S5 Bound States
• Massless $Ad{S}_2$ scattering and Bethe ansatz
• Large spin expansion of the long-range Baxter equation in the sl(2) sector of N=4 SYM
• Anomalous dimensions of finite size field strength operators in N=4 SYM
• $q$-Poincaré supersymmetry in $Ad{S}_5/CF{T}_4$
• The Tetrahedron Zamolodchikov Algebra and the AdS5 x S5 S-matrix
• The S-matrix of the Faddeev-Reshetikhin Model, Diagonalizability and PT Symmetry
• Yangians in Integrable Field Theories, Spin Chains and Gauge-String Dualities
• Nonlocal Symmetries and Factorized Scattering
• Dynamic Lattice Supersymmetry in gl(n|m) Spin Chains
• Testing the nested light-cone Bethe equations of the AdS_5 x S^5 superstring
• $q$-Poincaré invariance of the $Ad{S}_3/CF{T}_2$ $R$-matrix
• Boost generator in AdS_3 integrable superstrings for general braiding
• Integrability and the AdS/CFT correspondence
• Classical Exchange Algebra of the Superstring on S^5 with the AdS-time
• Contracted and expanded integrable structures
• An algebraic approach to the Hubbard model
• On $Ad{S}_2/CF{T}_1$ transfer matrices, Bethe ansatz and scale invariance
• On two-dimensional quasitopological field theories
• The Ising model and planar N=4 Yang-Mills
• The Quantum Affine Origin of the AdS/CFT Secret Symmetry
• Aspects of Integrability in N =4 SYM
• Geometry of Massless Scattering in Integrable Superstring
• 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)
• Matrix Reduction and the su(2|2) superalgebra in AdS/CFT
• PSU(2,2|4) Exchange Algebra of N=4 Superconformal Multiplets
• Classical Lie Bialgebras for AdS/CFT Integrability by Contraction and Reduction
• Constrained WZWN Models on G/{S x U(1)^n} and Exchange Algebra of G-Primaries
• Yangian Symmetry, S-Matrices and Bethe Ansatz for the AdS5 x S5 Superstring
• Multi-parametric R-matrix for the sl(2|1) Yangian
• Quantum Spectral Curve for AdS${}_3$/CFT${}_2$: a proposal
• Flag Integrable Models and Generalized Graded Algebras
• A study of integrable form factors in massless relativistic $Ad{S}_2$