T Duality and TT[over ¯]-like Deformations of Sigma Models

We initiate the study of the interplay between T duality and classical stress tensor deformations in two-dimensional sigma models. We first show that a general Abelian T duality commutes with the TT[over ¯] deformation, which can be engineered by a gravitational dressing. Then, by using an auxiliary field formulation of stress tensor deformations of the principal chiral model (PCM), we prove that non-Abelian T duality and arbitrary TT[over ¯]-like flows also commute for theories in this class. We argue that all such auxiliary field deformations of both the PCM and its T dual are classically integrable.