We construct a two-parameter deformation of the Metsaev-Tseytlin action for supercosets with isometry group of the form G x G. The resulting action is classically integrable and is Poisson-Lie symmetric suggesting that the symmetry of the model is q-
deformed, U_q_L(G) x U_q_R(G). Focusing on the cases relevant for strings moving in AdS_3 x S^3 x T^4 and AdS_3 x S^3 x S^3 x S^1, we analyze the corresponding deformations of the AdS_3 and S^3 metrics. We also construct a two-parameter $q$-deformation of the u(1) + psu(1|1)^2 x u(1) x R^3-invariant R-matrix and closure condition, which underlie the light-cone gauge S-matrix and dispersion relation of the aforementioned string theories. With the appropriate identification of parameters, the near-BMN limit of the dispersion relation is shown to agree with that found from the deformed supercoset sigma model.
We derive the exact S-matrix for the scattering of particular representations of the centrally-extended psu(1|1)^2 Lie superalgebra, conjectured to be related to the massive modes of the light-cone gauge string theory on AdS_2 x S^2 x T^6. The S-matr
ix consists of two copies of a centrally-extended psu(1|1) invariant S-matrix and is in agreement with the tree-level result following from perturbation theory. Although the overall factor is left unfixed, the constraints following from crossing symmetry and unitarity are given. The scattering involves long representations of the symmetry algebra, and the relevant representation theory is studied in detail. We also discuss Yangian symmetry and find it has a standard form for a particular limit of the aforementioned representations. This has a natural interpretation as the massless limit, and we investigate the corresponding limits of the massive S-matrix. Under the assumption that the massless modes of the light-cone gauge string theory transform in these limiting representations, the resulting S-matrices would provide the building blocks for the full S-matrix. Finally, some brief comments are given on the Bethe ansatz.
