Hollowood, Timothy J.Miramontes Antas, José Luis2020-04-142020-04-142014Hollowood, T. and Miramontes, J., 2014. Symplectic deformations of integrable field theories and AdS/CFT. Physics Letters B, 739, 214-2170370-2693http://hdl.handle.net/10347/21366Relativistic 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 AdS5×S5eng©2014 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/3.0/)http://creativecommons.org/licenses/by/3.0/journal article10.1016/j.physletb.2014.10.0601873-2445open access