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.