2009/02/13 by Timothy J. Hollowood, J. Luis Miramontes · 60 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Classical mechanics #Computer science #Context (archaeology) #Cosmology and Gravitation Theories #Dimensional reduction #Equations of motion #Geometry #Magnon #Mathematical physics #Mathematics #Motion (physics) #Nonlinear Waves and Solitons #Nonlinear system #Physics #Quantum mechanics #Reduction (mathematics) #Sigma #Sigma model #Sine #Soliton #Space (punctuation) #String (physics) #Theoretical physics #Transformation (genetics) #hep-th #sine-Gordon equation
paper · pdf · doi:10.1088/1126-6708/2009/04/060
published in Journal of High Energy Physics 2009(04), 060 (Springer Nature) · 52 pages
arxiv created 2009/02/13 · openalex publication_date 2009/04/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 Sn, CPn 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 CP3. 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.