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

Author:
Benoît Vicedo (12) diet.bovine.co@gmail.com  


Journal:
Letters in Mathematical Physics


Issue Date:
2011


Abstract(summary):

The classical integrable structure of \mathbbZ4{\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 \mathbbZ4{\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.


Page:
249-274


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