A bstract We study the deformed AdS ~(5)× S _(5)supercoset model of arXiv:1309.5850 which depends on one parameter κ and has classical quantum group symmetry. We confirm the conjecture that in the “maximal” deformation limit, κ → ∞, this model is T-dual to “flipped” double Wick rotation of the target space AdS ~(5)× S _(5), i.e. dS ~(5)× H _(5)space supported by an imaginary 5-form flux. In the imaginary deformation limit, κ → i , the corresponding target space metric is of a pp-wave type and thus the resulting light-cone gauge S-matrix becomes relativistically invariant. Omitting non-unitary contributions of imaginary WZ terms, we find that this tree-level S-matrix is equivalent to that of the generalized sine-Gordon model representing the Pohlmeyer reduction of the undeformed AdS ~(5)× S _(5)superstring model. We also study in some detail similar deformations of the AdS ~(3)× S _(3)and AdS ~(2)× S _(2)supercosets. The bosonic part of the deformed AdS ~(3)× S _(3)model happens to be equivalent to the symmetric case of the sum of the Fateev integrable deformation of the SL(2) and SU(2) principal chiral models, while in the AdS ~(2)× S _(2)case the role of the Fateev model is played by the 2d “sausage” model. The κ = i limits are again directly related to the Pohlmeyer reductions of the corresponding AdS ~( n )× S _( n )supercosets: (2,2) super sine-Gordon model and its complex sine-Gordon analog. We also discuss possible deformations of AdS ~(3)× S _(3)with more than one parameter.
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