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arXiv · hep-th/0701281

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

Alessandro Torrielli
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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.

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Alessandro Torrielli. 2007-04-25. Classical r-matrix of the su(2|2) SYM spin-chain. https://doi.org/10.1103/physrevd.75.105020

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