We study the classical spectrum of string theory on AdS 5 × S 5 in the Hofman-Maldacena limit. We find a family of classical solutions corresponding to Giant Magnons with two independent angular momenta on S 5 . These solutions are related via Pohlmeyer's reduction procedure to the charged solitons of the Complex sine-Gordon equation. The corresponding string states are dual to BPS boundstates of many magnons in the spin-chain description of planar N = 4 SUSY Yang-Mills.The exact dispersion relation for these states is obtained from a purely classical calculation in string theory.
We study the conjectured exact S-matrix for the scattering of BPS magnon boundstates in the spin-chain description of planar N = 4 SUSY Yang-Mills. The conjectured S-matrix exhibits both simple and double poles at complex momenta. Some of these poles lie parametrically close to the real axis in momentum space on the branch where particle energies are positive. We show that all such poles are precisely accounted for by physical processes involving one or more on-shell intermediate particles belonging to the known BPS spectrum.
We study a family of classical string solutions with large spins on R t S 3 subspace of AdS 5 S 5 background, which are related to Complex sine-Gordon solitons via Pohlmeyer's reduction. The equations of motion for the classical strings are cast into Lamé equations and Complex sine-Gordon equations. We solve them under periodic boundary conditions, and obtain analytic profiles for the closed strings. They interpolate two kinds of known rigid configurations with two spins: on one hand, they reduce to folded or circular spinning/rotating strings in the limit where a soliton velocity goes to zero, while on the other hand, the dyonic giant magnons are reproduced in the limit where the period of a kink-array goes to infinity.
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