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.

19 pages, no figures

References in corpus (12)

• Giant Magnons
• The AdS_5xS^5 superstring worldsheet S-matrix and crossing symmetry
• Quantum corrections to the string Bethe ansatz
• On AdS_5 x S^5 String S-matrix
• On the Singularities of the Magnon S-matrix
• Infinite spin limit of semiclassical string states
• A Universality Test of the Quantum String Bethe Ansatz
• Single spike solutions for strings on S2 and S3
• Constructing the AdS/CFT dressing factor
• Strings as Multi-Particle States of Quantum Sigma-Models
• Interacting finite-size magnons
• Baecklund transformations, energy shift and the plane wave limit

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• Pohlmeyer-reduced form of string theory in AdS_5 x S^5: semiclassical expansion
• Dressed Giant Magnons on CP^3
• Spatial 't Hooft loop in hot SUSY theories at weak coupling
• AdS String: Classical Solutions and Moduli Dynamics