Classical r-matrix of the su(2|2) SYM spin-chain

Abstract

In this note we straightforwardly derive and make use of the quantum R-matrix for the su(2|2) SYM spin-chain in the manifest su(1|2)-invariant formulation, which solves the standard quantum Yang-Baxter equation, in order to obtain the correspondent (undressed) classical r-matrix from the first order expansion in the ``deformation'' parameter 2 π/ \sqrtλ, and check that this last solves the standard classical Yang-Baxter equation. We analyze its bialgebra structure, its dependence on the spectral parameters and its pole structure. We notice that it still preserves an su(1|2) subalgebra, thereby admitting an expression in terms of a combination of projectors, which spans only a subspace of su(1|2) \otimes su(1|2). We study the residue at its simple pole at the origin, and comment on the applicability of the classical Belavin-Drinfeld type of analysis.

14 pages, LaTeX, no figures; corrections made, further analysis of the residue and references added

References in corpus (56)

• Strings in flat space and pp waves from $\mathcal{N}=4$ Super Yang Mills
• The Bethe-Ansatz for N=4 Super Yang-Mills
• Hidden Symmetries of the AdS_5 x S^5 Superstring
• Transcendentality and Crossing
• 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
• Giant Magnons
• The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory
• Multi-spin string solutions in AdS_5 x S^5
• A Novel Long Range Spin Chain and Planar N=4 Super Yang-Mills
• 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
• A Crossing-Symmetric Phase for AdS_5 x S^5 Strings
• Spinning strings in AdS_5 x S^5 and integrable systems
• Spinning strings in AdS_5 x S^5: new integrable system relations
• The Zamolodchikov-Faddeev Algebra for AdS_5 x S^5 Superstring
• Planar N=4 gauge theory and the Inozemtsev long range spin chain
• Quantum corrections to the string Bethe ansatz
• 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
• The Off-shell Symmetry Algebra of the Light-cone AdS_5 x S^5 Superstring
• On AdS_5 x S^5 String S-matrix
• A Test of the AdS/CFT Correspondence Using High-Spin Operators
• Magnon Bound States and the AdS/CFT Correspondence
• On Quantum Corrections to Spinning Strings and Bethe Equations
• Holography Beyond the Penrose Limit
• Dyonic Giant Magnons
• On the highest transcendentality in N=4 SUSY
• On the Singularities of the Magnon S-matrix
• Worldsheet Scattering in AdS_5 x S^5
• On Integrability of Classical SuperStrings in AdS_5 x S^5
• The AdS5xS5 Superstring in Light-Cone Gauge and its Bethe Equations
• On the Hopf algebra structure of the AdS/CFT S-matrix
• Connecting giant magnons to the pp-wave: An interpolating limit of $Ad{S}_5\times S^5$
• 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
• Stringy sums and corrections to the quantum string Bethe ansatz
• Higher Impurity AdS/CFT Correspondence in the Near-BMN Limit
• Bethe Ansatz in Stringy Sigma Models
• The magnon kinematics of the AdS/CFT correspondence
• Solutions to the Quantum Yang-Baxter Equation with Extra Non-Additive Parameters
• The Asymptotic Spectrum of the N=4 Super Yang-Mills Spin Chain
• q-Deformed Supersymmetry and Dynamic Magnon Representations
• The S-Matrix of AdS/CFT and Yangian Symmetry
• On the Scattering Phase for AdS_5 x S^5 Strings
• On the Scattering of Magnon Boundstates
• Yangian Symmetry at Two Loops for the su(2|1) Sector of N=4 SYM
• Integrability and non-perturbative effects in the AdS/CFT correspondence
• A construction for R-matrices without difference property in the spectral parameter

Cited by in corpus (36)

• On String S-matrix, Bound States and TBA
• Quantum Deformations of the One-Dimensional Hubbard Model
• The all-loop integrable spin-chain for strings on AdS_3 x S^3 x T^4: the massive sector
• The S-matrix of String Bound States
• The Classical r-matrix of AdS/CFT and its Lie Bialgebra Structure
• The Bound State S-Matrix for AdS5 x S5 Superstring
• On Drinfeld's second realization of the AdS/CFT su(2|2) Yangian
• A Secret Symmetry of the AdS/CFT S-matrix
• The Classical Exchange Algebra of AdS5 x S5 String Theory
• Current presentation for the double super-Yangian $DY(\mathfrak{gl}(m|n))$ and Bethe vectors
• Yangians, S-matrices and AdS/CFT
• A Quantum Affine Algebra for the Deformed Hubbard Chain
• Algebra of transfer-matrices and Yang-Baxter equations on the string worldsheet in AdS(5) x S(5)
• A Yangian Double for the AdS/CFT Classical r-matrix
• 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
• An Exceptional Algebraic Origin of the AdS/CFT Yangian Symmetry
• Factorized world-sheet scattering in near-flat AdS_5 x S^5
• The S-matrix algebra of the AdS2 X S2 superstring
• Secret Symmetries in AdS/CFT
• Weakly coupled N=4 Super Yang-Mills and N=6 Chern-Simons theories from u(2|2) Yangian symmetry
• Universal blocks of the AdS/CFT Scattering Matrix
• 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
• Maximally extended sl(2|2) as a quantum double
• Yangians in Integrable Field Theories, Spin Chains and Gauge-String Dualities
• Review of AdS/CFT Integrability, Chapter VI.2: Yangian Algebra
• Classical Exchange Algebra of the Superstring on S^5 with the AdS-time
• The Quantum Affine Origin of the AdS/CFT Secret Symmetry
• PSU(2,2|4) Exchange Algebra of N=4 Superconformal Multiplets
• Spin-chain with PSU(2|2)xU(1)^3 and Non-linear Sigma-model with D(2,1;gamma)
• Classical Lie Bialgebras for AdS/CFT Integrability by Contraction and Reduction
• Killing scalar of non-linear sigma models on G/H realizing the classical exchange algebra
• Constrained WZWN Models on G/{S x U(1)^n} and Exchange Algebra of G-Primaries