Towards a two-parameter q -deformation of AdS3×S3×M4AdS3×S3×M4 superstrings

We construct a two-parameter deformation of the Metsaev–Tseytlin action for supercosets with isometry group of the form Gˆ×Gˆ. The resulting action is classically integrable and is Poisson–Lie symmetric suggesting that the symmetry of the model is q  -deformed, UqL(Gˆ)×UqR(Gˆ). Focusing on the cases relevant for strings moving in AdS3×S3×T4AdS3×S3×T4 and AdS3×S3×S3×S1AdS3×S3×S3×S1, we analyze the corresponding deformations of the AdS3AdS3 and S3S3 metrics. We also construct a two-parameter q  -deformation of the u(1)psu(1|1)2⋉u(1)⋉R3u(1)psu(1|1)2⋉u(1)⋉R3-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.