N-body Dynamics of Giant Magnons in RxS2

Abstract

We pursue the question of multi-magnon dynamics, focusing on the simplest case of magnons moving on RxS2 and working at the semiclassical level. Through a Pohlmeyer reduction, the problem reduces to another well known integrable field theory, the sine-Gordon model, which can be exactly described through an N-body model of Calogero type. The two theories coincide at the level of equations of motion, but physical quantities like the energies (of magnons and solitons) and the associated phase shifts are different. We start from the equivalence of the two systems at the level of equations of motion and require that the new (string theory) model reproduces the correct magnon energies and the phase shift, both of which differ from the soliton case. From the comparison of energies we suggest a Hamiltonian, and from requiring the correct phase shift we are led to a nontrivial Poisson structure representing the magnons.

arXiv comment19 pages, no figures

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Cited by in corpus (7)

• Moduli Dynamics of AdS_3 Strings
• Pohlmeyer-reduced form of string theory in AdS_5 x S^5: semiclassical expansion
• Review of AdS/CFT Integrability, Chapter II.1: Classical AdS5xS5 string solutions
• Dressed Giant Magnons on CP^3
• Spatial 't Hooft loop in hot SUSY theories at weak coupling
• AdS String: Classical Solutions and Moduli Dynamics
• The Force Between Giant Magnons