I will discuss the so-called "eta-deformation" of strings on AdS5 x S5.
This is particularly interesting since it preserves the classical integrability of the original theory and it realises a q-deformation of its symmetry algebra.
In addition to the deformed metric also a B-field is generated, and a singularity appears at a finite radius of the deformed AdS space.
I will explain how we confirmed the q-deformation by matching the tree-level scattering on the worldsheet with the large tension limit of the S-matrix previously found by requiring psu_q(2|2) invariance.
I will also address the challenging question of whether we can embed the metric and B-field into a full type IIB supergravity background. This will be mainly done by computing the deformed Lagrangian at quadratic order in fermions and by resolving the novel complications introduced by the deformation procedure.
