A Yangian Double for the AdS/CFT Classical r-matrix

TL;DR

This paper reformulates the classical r-matrix of AdS/CFT using a Yangian double structure, shedding light on the underlying infinite-dimensional symmetry algebra and aiding in the construction of its universal R-matrix.

Contribution

It introduces a new Yangian double framework for the AdS/CFT classical r-matrix, revealing the algebraic structure and providing a basis for universal R-matrix construction.

Findings

Expressed the classical r-matrix in terms of an infinite generator family.

Derived the algebra's commutation relations for closure.

Suggested a universal form related to Yangian doubles.

Abstract

We express the classical r-matrix of AdS/CFT in terms of tensor products involving an infinite family of generators, which takes a form suggestive of the universal expression obtained from a Yangian double. This should provide an insight into the structure of the infinite dimensional symmetry algebra underlying the integrability of the model, and give a clue to the construction of its universal R-matrix. We derive the commutation relations under which the algebra of these new generators close.