Review of AdS/CFT Integrability, Chapter III.2: Exact World-Sheet S-Matrix

We review the derivation of the S-matrix for planar N = 4 supersymmetric Yang-Mills theory and type IIB superstring theory on an AdS ₅ × S ⁵ background. After deriving the S-matrix for the su(2) and su(3) sectors at the one-loop level based on coordinate Bethe ansatz, we show how su(2{pipe}2) symmetry leads to the exact asymptotic S-matrix up to an overall scalar function. We then briefly review the spectrum of bound states by relating these states to simple poles of the S-matrix. Finally, we review the derivation of the asymptotic Bethe equations, which can be used to determine the asymptotic multiparticle spectrum.