The Classical r-matrix of AdS/CFT and its Lie Bialgebra Structure

Abstract

In this paper we investigate the algebraic structure of AdS/CFT in the strong-coupling limit. We propose an expression for the classical r-matrix with (deformed) u(2|2) symmetry, which leads to a quasi-triangular Lie bialgebra as the underlying symmetry algebra. On the fundamental representation our r-matrix coincides with the classical limit of the quantum R-matrix.

31 pages, v2: added comment on classical double structure in 4.5. new section 5 on relation to other algebras (from old appendix and new results). fixed typos and mathematical inaccuracies, added references, v3: improved mathematical presentation, to appear in CMP

References in corpus (11)

• 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 Bethe ansatz approach for factorizable centrally extended S-matrices
• The AdS(5)xS(5) superstring quantum spectrum from the algebraic curve
• World-sheet scattering in AdS_5 x S^5 at two loops
• Classical r-matrix of the su(2|2) SYM spin-chain
• A Secret Symmetry of the AdS/CFT S-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
• Hidden Symmetries and Integrable Hierarchy of the N=4 Supersymmetric Yang-Mills Equations

Cited by in corpus (11)

• Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory
• Quantum Deformations of the One-Dimensional Hubbard Model
• The S-matrix of String Bound States
• The Classical Exchange Algebra of AdS5 x S5 String Theory
• Algebra of transfer-matrices and Yang-Baxter equations on the string worldsheet in AdS(5) x S(5)
• 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
• The su(2|3) Undynamic Spin Chain
• 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