| Summary: | Abstract In this paper, we regard the T T ¯ / J T ¯ $$ T\overline{T}/J\overline{T} $$ -deformed CFTs as perturbation theories and calculate the first order correction of the correlation functions due to the T T ¯ / J T ¯ $$ T\overline{T}/J\overline{T} $$ deformation. As applications, we study the Rényi entanglement entropy of excited state in the T T ¯ / J T ¯ $$ T\overline{T}/J\overline{T} $$ -deformed two-dimensional CFTs. We find, up to the first order perturbation of the deformation, the Rényi entanglement entropy of locally excited states will acquire a nontrivial time dependence. The excess of the Rényi entanglement entropy of locally excited state is changed up to order O(c). Furthermore, the out of time ordered correlation function is investigated to confirm that the T T ¯ / J T ¯ $$ T\overline{T}/J\overline{T} $$ -deformations do not change the maximal chaotic behavior of holographic CFTs up to the first order of the deformations.
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