Abstract
We consider giant magnons propagating in a ?-deformed AdS5 ? S5 background obtained from AdS5 ? S5 by means of a chain of TsT transformations. We point out that in the light-cone gauge and in the infinite J limit the deformed and undeformed string models share the same magnon dispersion relation, the (2|2)???(2|2)-invariant world-sheet S-matrix and the dressing factor. The ?-dependence in the limit is only due to different level-matching conditions. We consider the reduction of the deformed model to R ? S3 and determine the leading ?-dependence of the dispersion relation for a finite J giant magnon.
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