Symplectic Deformations of Integrable Field Theories and AdS/CFT

Abstract

Relativistic integrable field theories like the sine-Gordon equation have an infinite set of conserved charges. In a light-front formalism these conserved charges are closely related to the integrable modified KdV hierarchy at the classical level. The latter hierarchy admits a family of symplectic structures which we argue can be viewed as deformations of the relativistic sine-Gordon symplectic structure. These deformed theories are integrable but no longer relativistic and the basic excitations of the theory, the solitons, have an interesting non-relativistic dispersion relation that in a certain limit becomes the dispersion relation of dyonic giant magnons of string theory in the AdS/CFT correspondence. We argue that the deformed classical theories can be lifted to quantum theories when the sine-Gordon theory is embedded in a larger theory that describes the string world-sheet sigma model in AdS(5)xS(5).

4 pages

References in corpus (8)

• Pohlmeyer reduction of AdS_5 x S^5 superstring sigma model
• Magnon Bound States and the AdS/CFT Correspondence
• Pohlmeyer reduction revisited
• The Quantum Deformed Mirror TBA I
• Magnons, their Solitonic Avatars and the Pohlmeyer Reduction
• Sine-Gordon-like action for the Superstring in AdS(5) x S(5)
• The AdS(5)xS(5) Semi-Symmetric Space Sine-Gordon Theory
• Bound States of the q-Deformed AdS5 x S5 Superstring S-matrix

Cited by in corpus (4)

• Derivation of the action and symmetries of the q-deformed AdS_5 x S^5 superstring
• On deformations of AdS_n x S^n supercosets
• An Integrable Deformation of the AdS5 x S5 Superstring
• On the exact spectrum and mirror duality of the (AdS_5 x S^5)_eta superstring