On deformations of AdS_n x S^n supercosets

Abstract

We study the deformed AdS_5 x S^5 supercoset model of arXiv:1309.5850 which depends on one parameter kappa and has classical quantum group symmetry. We confirm the conjecture that in the "maximal" deformation limit kappa -> infinity this model is T-dual to "flipped" double Wick rotation of the target space AdS_5 x S^5, i.e. dS_5 x H^5 space supported by an imaginary 5-form flux. In the imaginary deformation limit, kappa -> 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 x S^5 superstring model. We also study in some detail similar deformations of the AdS_3 x S^3 and AdS_2 x S^2 supercosets. The bosonic part of the deformed AdS_3 x 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 x S^2 case the role of the Fateev model is played by the 2d "sausage" model. The kappa = i limits are again directly related to the Pohlmeyer reductions of the corresponding AdS_n x S^n supercosets: (2,2) super sine-Gordon model and its complex sine-Gordon analog. We also discuss possible deformations of AdS_3 x S^3 with more than one parameter.