Dyonic Giant Magnons

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We study the classical spectrum of string theory on AdS₅ X S⁵ in the Hofman-Maldacena limit. We find a family of classical solutions corresponding to Giant Magnons with two independent angular momenta on S⁵. 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.