Magnons, their Solitonic Avatars and the Pohlmeyer Reduction

Details Magnons, their Solitonic Avatars and the Pohlmeyer Reduction Magnons, their Solitonic Avatars and the Pohlmeyer Reduction

2009-02-13

arxiv.org/abs/0902.2405v1

JHEP 0904:060,2009

Physics

High Energy Physics

High Energy Physics - Theory

52 pages

Scientific paper

10.1088/1126-6708/2009/04/060

We study the solitons of the symmetric space sine-Gordon theories that arise once the Pohlmeyer reduction has been imposed on a sigma model with the symmetric space as target. Under this map the solitons arise as giant magnons that are relevant to string theory in the context of the AdS/CFT correspondence. In particular, we consider the cases S^n, CP^n and SU(n) in some detail. We clarify the construction of the charges carried by the solitons and also address the possible Lagrangian formulations of the symmetric space sine-Gordon theories. We show that the dressing, or Backlund, transformation naturally produces solitons directly in both the sigma model and the symmetric space sine-Gordon equations without the need to explicitly map from one to the other. In particular, we obtain a new magnon solution in CP^3. We show that the dressing method does not produce the more general "dyonic" solutions which involve non-trivial motion of the collective coordinates carried by the solitons.

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