Target space supergeometry of η and λ-deformed strings

We study the integrable η and λ-deformations of supercoset string sigma models, the basic example being the deformation of the AdS 5 × S 5 superstring. We prove that the kappa symmetry variations for these models are of the standard Green-Schwarz form, and we determine the target space supergeometry by computing the superspace torsion. We check that the λ-deformation gives rise to a standard (generically type II*) supergravity background; for the η-model the requirement that the target space is a supergravity solution translates into a simple condition on the R-matrix which enters the definition of the deformation. We further construct all such non-abelian R-matrices of rank four which solve the homogeneous classical Yang-Baxter equation for the algebra so (2, 4). We argue that most of the corresponding backgrounds are equivalent to sequences of non-commuting TsT-transformations, and verify this explicitly for some of the examples.