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Classical r matrix of the su(2|2) super Yang-Mills spin chain

Torrielli, A (2007) Classical r matrix of the su(2|2) super Yang-Mills spin chain Physical Review D - Particles, Fields, Gravitation and Cosmology, 75 (10).

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In this note we straightforwardly derive and make use of the quantum R matrix for the su(2|2) super Yang-Mills 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 2π/√λ 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)⊗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.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
Torrielli, A
Date : 2007
DOI : 10.1103/PhysRevD.75.105020
Additional Information : Copyright 2007 American Physical Society
Depositing User : Symplectic Elements
Date Deposited : 27 Jan 2012 12:21
Last Modified : 31 Oct 2017 14:17

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