Giant Magnons of String Theory in the Lambda Background

Abstract

The analogues of giant magnon configurations are studied on the string world sheet in the lambda background. This is a discrete deformation of the AdS(5)xS(5) background that preserves the integrability of the world sheet theory. Giant magnon solutions are generated using the dressing method and their dispersion relation is found. This reduces to the usual dyonic giant magnon dispersion relation in the appropriate limit and becomes relativistic in another limit where the lambda model becomes the generalized sine-Gordon theory of the Pohlmeyer reduction. The scattering of giant magnons is then shown in the semi-classical limit to be described by the quantum S-matrix that is a quantum group deformation of the conventional giant magnon S-matrix. It is further shown that in the small g limit, a sector of the S-matrix is related to the XXZ spin chain whose spectrum matches the spectrum of magnon bound states.

arXiv comment53 pages, 6 figures, final version to appear in JHEP

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• Poisson-Lie duals of the eta deformed symmetric space sigma model
• Holomorphic Chern-Simons theory and lambda models: PCM case
• Quantum Anisotropic Sigma and Lambda Models as Spin Chains
• Lambda Models From Chern-Simons Theories
• $\lambda$-Deformation Of The $Ad{S}_5\times S^5$ Pure Spinor Superstring
• Classical solutions of $\lambda$-deformed coset models
• Classical Spectral Curve of the AdS_5 x S^5 Lambda Superstring
• Integrability of the $\lambda$-deformation of the PCM with spectators