T Duality and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>T</mml:mi><mml:mover accent="true"><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mo stretchy="false">¯</mml:mo></mml:mrow></mml:mover></

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.