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).
Classical.pdf - Accepted version Manuscript
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.
|Divisions :||Faculty of Engineering and Physical Sciences > Mathematics|
|Identification Number :||https://doi.org/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 :||23 Sep 2013 18:57|
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