On the Singularities of the Magnon S-matrix

Details On the Singularities of the Magnon S-matrix On the Singularities of the Magnon S-matrix

2007-03-11

arxiv.org/abs/hep-th/0703104v2

Phys.Rev.D76:025011,2007

Physics

High Energy Physics

High Energy Physics - Theory

40 pages, 14 figures; typos corrected, references added

Scientific paper

10.1103/PhysRevD.76.025011

We investigate the analytic structure of the magnon S-matrix in the spin-chain description of planar ${\cal N}=4$ SUSY Yang-Mills/$AdS_{5}\times S^{5}$ 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 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 (hep-th/0609044 and hep-th/0610251). 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.

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