Magnon Bound States and the AdS/CFT Correspondence

We study the spectrum of asymptotic states in the spin-chain description of planar N=4 SUSY Yang-Mills. In addition to elementary magnons, the asymptotic spectrum includes an infinite tower of multi-magnon bound states with exact dispersion relation, Delta-J_{1} = sqrt{Q^{2}+(lambda/pi^2)sin^2(p/2)} where the positive integer Q is the number of constituent magnons. These states account precisely for the known poles in the exact S-matrix. They transform in the same small representation of supersymmetry as the elementary magnon and are present for all values of the 't Hooft coupling. At strong coupling we identify the dual states in semiclassical string theory