The correlation function of (1, 1) and (2, 2) supersymmetric theories with TT¯ deformation

Abstract

In the paper, we compute the correlation functions in 2D $\mathcal{N}$ = (1, 1) and $\mathcal{N}$ = (2, 2) superconformal field theories with $T\overline{T}$ deformation up to the first order of the deformation in terms of perturbation theory. With the help of superconformal Ward identity in $\mathcal{N}$ = (1, 1) and $\mathcal{N}$ = (2, 2) theories and careful regularization, the correlation functions in the deformed theory can be obtained up to the first order perturbation. This study is the extension from previous bosonic $T\overline{T}$ deformation to the supersymmetric one.