T-Duality and T T-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 T T 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 T T-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.