Giant Magnons in Symmetric Spaces: Explicit N-soliton solutions for CP^n, SU(n) and S^n

Abstract

Giant magnons are one of the main manifestations of integrability on the string theory side of the AdS/CFT correspondence. Motivated by the recent advances in their study, especially in the context of the string theory dual of ABJM theory, we present and prove explicit N-soliton solutions for the relevant CP^n, SU(n) and S^n sigma models. The proof is based on solving the dressing method recursion with the help of determinant operations, and our solutions hold for any choice of vacuum and soliton parameters. We further specialize our results for the choices that lead to giant magnons, and as an application, we calculate the classical time delay due to the scattering of an arbitrary number of CP^2 elementary dyonic magnons. The determinant expressions for our N-soliton solutions could possibly be used for the derivation of an effective particle description of magnon scattering.

34 pages. v2: typos corrected, references updated, clarifications added; to appear in JHEP

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• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• The Bethe ansatz for superconformal Chern-Simons
• The all loop AdS4/CFT3 Bethe ansatz
• Spin Chains in N=6 Superconformal Chern-Simons-Matter Theory
• Dyonic Giant Magnons
• Spinning strings at one-loop in AdS_4 x P^3
• Integrable Spin Chain in Superconformal Chern-Simons Theory
• Generating AdS String Solutions
• Dressing the Giant Magnon
• Solitons and AdS String Solutions
• Magnons, their Solitonic Avatars and the Pohlmeyer Reduction
• Quantum Scattering of Giant Magnons
• A New and Elementary CP^n Dyonic Magnon
• Semiclassical Quantization of the Giant Magnon
• Dressing the Giant Gluon
• Dressed Giant Magnons on CP^3
• Giant Magnons on CP^3 by Dressing Method
• Exact solutions for N-magnon scattering

Cited by in corpus (8)

• Comment on Strings in AdS3 x S3 x S3 x S1 at One Loop
• Quantum Strings and the AdS4/CFT3 Interpolating Function
• The Relativistic Avatars of Giant Magnons and their S-Matrix
• Dressed Wilson Loops on S^2
• Pohlmeyer reduction and Darboux transformations in Euclidean worldsheet AdS_3
• Generating string solutions in BTZ
• Divergent energy strings in $Ad{S}_5\times S^5$ with three angular momenta
• Classical strings in $Ad{S}_4\times {\mathbb{CP}}^3$ with three angular momenta