On the Singularities of the Magnon S-matrix

TL;DR

This paper analyzes the analytic structure of the magnon S-matrix in planar ${ m N}=4$ SYM, revealing double poles from BPS magnon pairs that match conjectured locations, clarifying the nature of these singularities.

Contribution

It demonstrates that the large family of poles in the magnon S-matrix are double poles from BPS magnon pairs, confirming conjectured pole locations and clarifying their physical significance.

Findings

Poles are double poles from BPS magnon pairs.

Pole locations are fixed by the BPS dispersion relation.

No new bound states are indicated by these poles.

Abstract

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.