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Tseytlin, “Treelevel Smatrix of Pohlmeyer reduced form
 of AdS5 × S5 superstring theory,” JHEP 1002 (2010) 094 [arXiv:0912.2958
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Interacting finitesize magnons
 J. Phys. A41
"... We explicitly construct a large class of finitevolume twomagnon string solutions moving on × S2. In particular, by making use of the relationship between the O(3) sigma model and sineGordon theory we are able to find solutions corresponding to the periodic analogues of magnon scattering and breat ..."
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We explicitly construct a large class of finitevolume twomagnon string solutions moving on × S2. In particular, by making use of the relationship between the O(3) sigma model and sineGordon theory we are able to find solutions corresponding to the periodic analogues of magnon scattering and breatherlike solutions. After semiclassically quantizing these solutions we invert the implicit expressions for the excitation energies in certain limits and find the corrections for the multimagnon states. For the breatherlike solutions we express the energies directly in terms of the action variable whereas for the scattering solution we express the result as a combination of corrections
ImperialTPBH201001 On the perturbative Smatrix of generalized sineGordon models
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Exact solutions for Nmagnon scattering
 JHEP
, 2008
"... Abstract: Giant magnon solutions play an important role in various aspects of the AdS/CFT correspondence. We apply the dressing method to construct an explicit formula for scattering states of an arbitrary number N of magnons on R × S 3. The solution can be written in Hirota form and in terms of det ..."
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Abstract: Giant magnon solutions play an important role in various aspects of the AdS/CFT correspondence. We apply the dressing method to construct an explicit formula for scattering states of an arbitrary number N of magnons on R × S 3. The solution can be written in Hirota form and in terms of determinants of N ×N matrices. Such a representation may prove useful for the construction of an effective particle Hamiltonian describing magnon dynamics.
Nbody Dynamics of Giant Magnons in R × S²
, 2008
"... We pursue the question of multimagnon dynamics, focusing on the simplest case of magnons moving on R × S² and working at the semiclassical level. Through a Pohlmeyer reduction, the problem reduces to another well known integrable field theory, the sineGordon model, which can be exactly described t ..."
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We pursue the question of multimagnon dynamics, focusing on the simplest case of magnons moving on R × S² and working at the semiclassical level. Through a Pohlmeyer reduction, the problem reduces to another well known integrable field theory, the sineGordon model, which can be exactly described through an Nbody 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.
Departamento de Física de Partículas, and
, 808
"... Abstract: A systematic group theoretical formulation of the Pohlmeyer reduction is presented. It provides a map between the equations of motion of sigma models with targetspace a symmetric space M = F/G and a class of integrable multicomponent generalizations of the sineGordon equation. When M is ..."
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Abstract: A systematic group theoretical formulation of the Pohlmeyer reduction is presented. It provides a map between the equations of motion of sigma models with targetspace a symmetric space M = F/G and a class of integrable multicomponent generalizations of the sineGordon equation. When M is of definite signature their solutions describe classical bosonic string configurations on the curved spacetime Rt × M. In contrast, if M is of indefinite signature the solutions to those equations can describe bosonic string configurations on Rt × M, M × S1 ϑ or simply M. The conditions required to enable the Lagrangian formulation of the resulting equations in terms of gauged WZW actions with a potential term are clarified, and it is shown that the corresponding Lagrangian action is not unique in general. The Pohlmeyer reductions of sigma models on CP n and AdSn are discussed as particular examples of symmetric spaces of definite and indefinite signature, respectively.
CERNPHTH/2006140 IFTUAM/CSIC0640
, 2006
"... hep–th/0608029 The magnon kinematics of the AdS/CFT correspondence ..."
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