Singularities of the magnonSmatrix

We investigate the analytic structure of the magnon $S$ matrix in the spin-chain description of planar $\mathcal{N}=4$ SUSY Yang-Mills/${\mathrm{AdS}}_5\times S^5$ strings. Semiclassical analysis suggests that the exact $S$ matrix must have a large family of poles near the real axis in momentum space. In this article we show that these are double poles corresponding to the exchange of pairs of Bogomol’nyi-Prasad-Sommerfield (BPS) magnons. Their locations in the complex plane are uniquely fixed by the known dispersion relation for the BPS particles. The locations precisely agree with the recent conjecture for the $S$ matrix by Beisert, Hernandez, Lopez, Eden, and Staudacher ( J. High Energy Phys. 11 (2006) 070 and J. Stat. Mech. 01 (2007) P021). These poles do not signal the presence of new bound states. In fact, a certain non-BPS localized classical solution, which was thought to give rise to new bound states, can actually decay into a pair of BPS magnons.