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We review the derivation of the S-matrix for planar N=4 supersymmetricYang-Mills theory and type IIB superstring theory on an AdS5xS5 background.After deriving the S-matrix for the su(2) and su(3) sectors at the one-looplevel based on coordinate Bethe ansatz, we show how su(2|2) symmetry leads tothe exact asymptotic S-matrix up to an overall scalar function. We then brieflyreview the spectrum of bound states by relating these states to simple poles ofthe S-matrix. Finally, we review the derivation of the asymptotic Betheequations, which can be used to determine the asymptotic multiparticlespectrum.

Review of AdS/CFT Integrability, Chapter III.2: Exact world-sheet S-matrix