Bound states, Yangian symmetry and classical r-matrix for the AdS5 × S5 superstring

We show that the recently found S-matrices describing the scattering of two-particle bound states of the light-cone string sigma model on AdS₅ × S⁵ are compatible with Yangian symmetry. In case the invariance with respect to the centrally extended algebra is not sufficient to fully specify the scattering matrix, the requirement of Yangian symmetry provides an alternative to the Yang-Baxter equation and leads to a complete, up to an overall phase, determination of the S-matrix. We then compare the semi-classical limit of the bound state S-matrices with the universal classical r-matrix by Beisert and Spill evaluated in the corresponding bound state representations and find perfect agreement.