The S-Matrix of Planar AdS/CFT

Recent years have brought about tremendous progress in understanding and computing the planar spectrum of N=4 gauge theory and IIB superstrings on AdS5xS5. The key insight is the apparent exact integrability of both models. I will present the scattering matrix in the excitation picture. The residual symmetry in this picture consists of two copies of SU(2|2) with central extensions. A remarkable property of the representation theory of centrally extended SU(2|2) leads to a unique invariant S-matrix which satisfies the Yang-Baxter equation. I will then discuss several aspects of the S-matrix such as its diagonalisation, crossing symmetry, transfer matrices as well as a curious relationship to Shastry's R-Matrix for the Hubbard chain.