On deformations of AdS (n) x S (n) supercosets - Hoare,B; Roiban,R; Tseytlin,AA (The Journal of High Energy Physics, 2014)
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.