Supersymmetric JTbar and TJbar deformations

We explore the JT ̄ and TJ ̄ deformations of two-dimensional field theories possessing N = (0, 1), (1, 1) and (0, 2) supersymmetry. Based on the stress-tensor and flavor current multiplets, we construct various bilinear supersymmetric primary operators that induce the J T ̄/T J ̄ deformation in a manifestly supersymmetric way. Moreover, their supersymmetric descendants are shown to agree with the conventional JT ̄/TJ ̄ operator on-shell. We also present some examples of J T ̄/T J ̄ flows arising from the supersymmetric deformation of free theories. Finally, we observe that all the deformation operators fit into a general pattern which generalizes the Smirnov-Zamolodchikov type composite operators.