Research output: Contribution to journal › Article › peer-review

**Classical r-matrix of the su(2|2) SYM spin-chain.** / Torrielli, Alessandro.

Research output: Contribution to journal › Article › peer-review

Torrielli, A 2007, 'Classical r-matrix of the su(2|2) SYM spin-chain', *Phys.Rev.D*, vol. 75, pp. 105020. https://doi.org/10.1103/PhysRevD.75.105020

Torrielli, A. (2007). Classical r-matrix of the su(2|2) SYM spin-chain. *Phys.Rev.D*, *75*, 105020. https://doi.org/10.1103/PhysRevD.75.105020

Torrielli A. Classical r-matrix of the su(2|2) SYM spin-chain. Phys.Rev.D. 2007 Jan 30;75:105020. https://doi.org/10.1103/PhysRevD.75.105020

@article{25c8808707064683ab6a9f28b4aa5305,

title = "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 \pi / \sqrt{\lambda}, 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.",

keywords = "hep-th",

author = "Alessandro Torrielli",

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

year = "2007",

month = jan,

day = "30",

doi = "10.1103/PhysRevD.75.105020",

language = "English",

volume = "75",

pages = "105020",

journal = "Phys.Rev.D",

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TY - JOUR

T1 - Classical r-matrix of the su(2|2) SYM spin-chain

AU - Torrielli, Alessandro

N1 - 14 pages, LaTeX, no figures; corrections made, further analysis of the residue and references added

PY - 2007/1/30

Y1 - 2007/1/30

N2 - 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 \pi / \sqrt{\lambda}, 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.

AB - 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 \pi / \sqrt{\lambda}, 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.

KW - hep-th

U2 - 10.1103/PhysRevD.75.105020

DO - 10.1103/PhysRevD.75.105020

M3 - Article

VL - 75

SP - 105020

JO - Phys.Rev.D

JF - Phys.Rev.D

ER -