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The Classical R-Matrix of AdS/CFT and its Lie Dialgebra Structure

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Abstract

The classical integrable structure of \({\mathbb{Z}_4}\)-graded supercoset σ-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 \({\mathbb{Z}_4}\)-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 σ-model can be understood as stemming from this latter twist since it leads to a non-skew-symmetric R-matrix.

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  1. Laboratoire de Physique Théorique, École Normale Supérieure, 24 rue Lhomond, 75231, Paris Cedex-5, France

    Benoît Vicedo

  2. Institut de Physique Théorique, C.E.A.-Saclay, 91191, Gif-sur-Yvette, France

    Benoît Vicedo

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Vicedo, B. The Classical R-Matrix of AdS/CFT and its Lie Dialgebra Structure. Lett Math Phys 95, 249–274 (2011). https://doi.org/10.1007/s11005-010-0446-9

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