Bound States, Yangian Symmetry and Classical r-matrix for the AdS5 x S5 Superstring

TL;DR

This paper demonstrates that the S-matrices for two-particle bound states in the AdS5 x S5 superstring model are compatible with Yangian symmetry, providing a complete determination of the scattering matrix and confirming agreement with the classical r-matrix in the semi-classical limit.

Contribution

It shows that Yangian symmetry can fully determine the bound state S-matrix, offering an alternative to the Yang-Baxter equation, and confirms the match with the classical r-matrix.

Findings

S-matrices are compatible with Yangian symmetry.

Yangian symmetry determines the S-matrix up to an overall phase.

Semi-classical limit matches the classical r-matrix.

Abstract

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 x S5 are compatible with Yangian symmetry. In case the invariance with respect to the centrally extended su(2|2) 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.