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In the paper, based on recent studies on $T\bar{T}$ deformation of 2D fieldtheory with supersymmetry, we investigate the deformed correlation functions in$\mathcal{N}=(1,1)$ and $\mathcal{N}=(2,2)$ 2D superconformal field theories.Up to the leading order in perturbation theory, we compute the correlationfunctions under $T\bar{T}$ deformation. The correlation functions in theseundeformed theories are almost known, and together with the help ofsuperconformal Ward identity in $\mathcal{N}=(1,1)$ and $\mathcal{N}=(2,2)$theories respectively we can obtain the correlation functions with operator$T\bar{T}$ inserted. Finally, by employing dimensional regularization, we canwork out the integrals in the first order perturbation. The study in this paperextends previous works on the correlation functions of $T\bar{T}$ deformedbosonic CFT to the supersymmetric case.

The correlation function of (1,1) and (2,2) supersymmetric theories with $T\bar{T}$ deformation