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

Benoit Vicedo

doi:10.1007/s11005-010-0446-9

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arXiv · 1003.1192

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

Benoit Vicedo

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Abstract

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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Benoit Vicedo. 2010-08-18. The classical R-matrix of AdS/CFT and its Lie dialgebra structure. https://doi.org/10.1007/s11005-010-0446-9

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