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

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• The Large N Limit of Superconformal Field Theories and Supergravity
• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Semiclassical quantization of rotating superstring in AdS_5 x S^5
• Giant Magnons
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• Magnon Bound States and the AdS/CFT Correspondence
• Dyonic Giant Magnons
• The Symmetric Space and Homogeneous sine-Gordon Theories
• Finite-size corrections in the SU(2) x SU(2) sector of type IIA string theory on AdS_4 x CP^3
• Lagrangian Formulation of Symmetric Space sine-Gordon Models
• Dressing the Giant Magnon
• Pohlmeyer reduction revisited
• Semiclassical Bethe Ansatz and AdS/CFT
• Quantum scattering of charged solitons in the complex sine-Gordon model
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• Dressing the Giant Magnon II
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• Duality in Complex sine-Gordon Theory
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• Dressing the Giant Gluon
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Cited by in corpus (47)

• An Integrable Deformation of the AdS5 x S5 Superstring
• Integrable Deformations of Strings on Symmetric Spaces
• Review of AdS/CFT Integrability, Chapter IV.3: N=6 Chern-Simons and Strings on AdS4xCP3
• q-Deformation of the AdS5 x S5 Superstring S-matrix and its Relativistic Limit
• Simplifying superstring and D-brane actions in AdS(4) x CP(3) superbackground
• Towards the quantum S-matrix of the Pohlmeyer reduced version of AdS_5 x S^5 superstring theory
• Quantum Strings and the AdS4/CFT3 Interpolating Function
• Restoring Unitarity in the q-Deformed World-Sheet S-Matrix
• Pohlmeyer-reduced form of string theory in AdS_5 x S^5: semiclassical expansion
• A Relativistic Relative of the Magnon S-Matrix
• Dyonic Giant Magnons in CP^3: Strings and Curves at Finite J
• On the perturbative S-matrix of generalized sine-Gordon models
• A New and Elementary CP^n Dyonic Magnon
• Review of AdS/CFT Integrability, Chapter II.1: Classical AdS5xS5 string solutions
• Giant Magnons in AdS4 x CP3: Embeddings, Charges and a Hamiltonian
• Self-accelerating Massive Gravity: Superluminality, Cauchy Surfaces and Strong Coupling
• Dressed Giant Magnons on CP^3
• Giant Magnons on CP^3 by Dressing Method
• Classical and Quantum Solitons in the Symmetric Space Sine-Gordon Theories
• Supersymmetry Flows, Semi-Symmetric Space Sine-Gordon Models And The Pohlmeyer Reduction
• Secret Symmetries in AdS/CFT
• The Relativistic Avatars of Giant Magnons and their S-Matrix
• The Semi-Classical Spectrum of Solitons and Giant Magnons
• Minimal surfaces in AdS space and Integrable systems
• Quantum finite-size effects for dyonic magnons in the AdS_4 x CP^3
• On Elliptic String Solutions in AdS(3) and dS(3)
• Scattering of Giant Magnons in CP^3
• General Leznov-Savelev solutions for Pohlmeyer reduced AdS${}_5$ minimal surfaces
• One-loop corrections to AdS_5 x S^5 superstring partition function via Pohlmeyer reduction
• Giant Magnons of String Theory in the Lambda Background
• Integrability vs Supersymmetry: Poisson Structures of The Pohlmeyer Reduction
• Symplectic Deformations of Integrable Field Theories and AdS/CFT
• Giant Magnons in Symmetric Spaces: Explicit N-soliton solutions for CP^n, SU(n) and S^n
• A Connection between Twistors and Superstring Sigma Models on Coset Superspaces
• Dressed Elliptic String Solutions on RxS^2
• Salient Features of Dressed Elliptic String Solutions on $\mathbb{R}\times$S${}^2$
• Stability Analysis of Classical String Solutions and the Dressing Method
• Spiky strings in de Sitter space
• Real and Virtual Bound States in Lüscher Corrections for CP3 Magnons
• Giant magnons and non-maximal giant gravitons
• Giant Spinons
• Boundary Giant Magnons and Giant Gravitons
• The Dressing Method as Non Linear Superposition in Sigma Models
• Towards a quadratic Poisson algebra for the subtracted classical monodromy of Symmetric Space Sine-Gordon theories
• Solving formally the Auxiliary System of $O(N)$ Non Linear Sigma Model
• Novel aspects of integrability for NLSMs in symmetric spaces
• Classical strings in $Ad{S}_4\times {\mathbb{CP}}^3$ with three angular momenta