An action variable of the sine-Gordon model

Abstract

It was conjectured that the classical bosonic string in AdS times a sphere has a special action variable which corresponds to the length of the operator on the field theory side. We discuss the analogous action variable in the sine-Gordon model. We explain the relation between this action variable and the Backlund transformations and show that the corresponding hidden symmetry acts on breathers by shifting their phase. It can be considered a nonlinear analogue of splitting the solution of the free field equations into the positive- and negative-frequency part.

arXiv commentv3,4: added explanations, discussion of O(N) sigma-model in section 5 v5: correction in the Introduction, small changes

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• Finite-size Effects from Giant Magnons
• Pohlmeyer reduction of AdS_5 x S^5 superstring sigma model
• Dyonic Giant Magnons
• Reflecting magnons
• Dressing the Giant Magnon
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• Interacting finite-size magnons
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• Exact solutions for N-magnon scattering
• The Structure of Non-Abelian Kinks
• Giant Magnons under NS-NS and Melvin Fields
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• Conformal SO(2,4) Transformations for the Helical AdS String Solution
• Pohlmeyer reduction for superstrings in AdS space
• Nonlinear quantum-mechanical system associated with Sine-Gordon equation in (1+2) dimensions