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

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

In: Phys.Rev.D, Vol. 75, 30.01.2007, p. 105020.

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Harvard

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

APA

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

Vancouver

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

Author

Torrielli, Alessandro. / Classical r-matrix of the su(2|2) SYM spin-chain. In: Phys.Rev.D. 2007 ; Vol. 75. pp. 105020.

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@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 -