T(T)over-bar deformation in SCFTs and integrable supersymmetric theories

We calculate the S-multiplets for two-dimensional Euclidean N = (0, 2) and N = (2, 2) superconformal field theories under the T (T) over bar deformation at leading order of perturbation theory in the deformation coupling. Then, from these N = (0, 2) deformed multiplets, we calculate two- and three-point correlators. We show the N = (0, 2) chiral ring's elements do not flow under the T (T) over bar deformation. Specializing to integrable supersymmetric seed theories, such as N = (2, 2) Landau-Ginzburg models, we use the thermodynamic Bethe ansatz to study the S-matrices and ground state energies. From both an S-matrix perspective and Melzer's folding prescription, we show that the deformed ground state energy obeys the inviscid Burgers' equation. Finally, we show that several indices independent of D-term perturbations including the Witten index, Cecotti-Fendley-Intriligator-Vafa index and elliptic genus do not flow under the T (T) over bar deformation.