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

TL;DR

This paper formulates the integrable structure of supercoset sigma-models in AdS/CFT using an R-matrix approach, revealing how the Zhukovsky map twist explains non-ultralocality and the Lie dialgebra structure.

Contribution

It introduces a novel R-matrix framework incorporating the Zhukovsky map twist to describe the integrable structure of AdS/CFT supercoset models.

Findings

The R-matrix approach captures the classical integrability of the models.

The Zhukovsky map twist is essential for the correct Lax matrix formulation.

Non-ultralocality arises from the non skew-symmetric R-matrix induced by the twist.

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.