Magnons, their Solitonic Avatars and the Pohlmeyer Reduction

Abstract

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.

52 pages

References in corpus (2)

• Spinning strings and AdS/CFT duality
• Pohlmeyer reduction of AdS_5 x S^5 superstring sigma model

Cited by in corpus (4)

• Pohlmeyer-reduced form of string theory in AdS_5 x S^5: semiclassical expansion
• A New and Elementary CP^n Dyonic Magnon
• Dressed Giant Magnons on CP^3
• Giant Magnons on CP^3 by Dressing Method