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 (3)

• Spinning strings and AdS/CFT duality
• On the Singularities of the Magnon S-matrix
• q-Deformed Supersymmetry and Dynamic Magnon Representations

Cited by in corpus (5)

• Quantum Deformations of the One-Dimensional Hubbard Model
• The S-matrix of String Bound States
• Algebra of transfer-matrices and Yang-Baxter equations on the string worldsheet in AdS(5) x S(5)
• q-Deformed Supersymmetry and Dynamic Magnon Representations
• Factorized world-sheet scattering in near-flat AdS_5 x S^5