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 (7)

• The AdS_5xS^5 superstring worldsheet S-matrix and crossing symmetry
• Quantum corrections to the string Bethe ansatz
• Spinning strings and AdS/CFT duality
• On AdS_5 x S^5 String S-matrix
• The AdS5xS5 Superstring in Light-Cone Gauge and its Bethe Equations
• A Universality Test of the Quantum String Bethe Ansatz
• On the Scattering Phase for AdS_5 x S^5 Strings

Cited by in corpus (28)

• On String S-matrix, Bound States and TBA
• The Off-shell Symmetry Algebra of the Light-cone AdS_5 x S^5 Superstring
• Quantum Deformations of the One-Dimensional Hubbard Model
• Connecting giant magnons to the pp-wave: An interpolating limit of $Ad{S}_5\times S^5$
• The Classical r-matrix of AdS/CFT and its Lie Bialgebra Structure
• Classical r-matrix of the su(2|2) SYM spin-chain
• A Secret Symmetry of the AdS/CFT S-matrix
• A Yangian Double for the AdS/CFT Classical r-matrix
• 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
• Landau-Lifshitz sigma-models, fermions and the AdS/CFT correspondence
• Reciprocity of gauge operators in N=4 SYM
• Semiclassical Quantization of the Giant Magnon
• Weakly coupled N=4 Super Yang-Mills and N=6 Chern-Simons theories from u(2|2) Yangian symmetry
• The su(2|3) Undynamic Spin Chain
• Universal blocks of the AdS/CFT Scattering Matrix
• Serre Relation and Higher Grade Generators of the AdS/CFT Yangian Symmetry
• Structure of the string R-matrix
• The Bethe Ansatz for AdS5 x S5 Bound States
• 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
• The S-matrix of the Faddeev-Reshetikhin Model, Diagonalizability and PT Symmetry
• Integrability and the AdS/CFT correspondence
• Contracted and expanded integrable structures
• The Ising model and planar N=4 Yang-Mills
• Aspects of Integrability in N =4 SYM
• Matrix Reduction and the su(2|2) superalgebra in AdS/CFT
• Yangian Symmetry, S-Matrices and Bethe Ansatz for the AdS5 x S5 Superstring