Deformations of AdS superstrings and Weyl symmetry

In this talk I will discuss recent developments in understanding the Weyl invariance (or lack thereof) of integrable deformations of AdS superstrings. One well-known example of such a deformation is the TsT transformation, which involves a T-duality, a shift introducing the deformation parameter, and a reverse T-duality. After introducing the deformed model, I will present two alternative constructions: (i) as a non-abelian duality, and (ii) as a homogeneous Yang-Baxter deformation. In the second part of the talk I will outline how this extends to a general relationship between non-abelian duality and homogeneous Yang-Baxter deformations, and discuss the consequences for the Weyl invariance of the deformed models. Depending on time I will also touch on the extent to which these results can be extended to the inhomogeneous Yang-Baxter deformation, a.k.a. the eta or q deformation.