On correlators in $T\overline{T}$-deformed conformal field theories

We consider the effect of $T\overline T$-deformations in conformal field theories within the perturbation theory. A dimensional regularization scheme is used for a perturbative calculation of the contribution of the $T\overline T$-deformation to the correlation functions of primary fields of conformal field theory. Renormalization of fields in the case of a two-point correlation function is presented.