The classical R-matrix of AdS/CFT and its Lie dialgebra structure

Details The classical R-matrix of AdS/CFT and its Lie dialgebra structure The classical R-matrix of AdS/CFT and its Lie dialgebra structure

2010-03-05

arxiv.org/abs/1003.1192v2

Lett.Math.Phys.95:249-274,2011

Physics

High Energy Physics

High Energy Physics - Theory

22 pages, 2 figures

Scientific paper

10.1007/s11005-010-0446-9

The classical integrable structure of Z_4-graded supercoset sigma-models, arising in the AdS/CFT correspondence, is formulated within the R-matrix approach. The central object in this construction is the standard R-matrix of the Z_4-twisted loop algebra. However, in order to correctly describe the Lax matrix within this formalism, the standard inner product on this twisted loop algebra requires a further twist induced by the Zhukovsky map, which also plays a key role in the AdS/CFT correspondence. The non-ultralocality of the sigma-model can be understood as stemming from this latter twist since it leads to a non skew-symmetric R-matrix.

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