Correlation functions, entanglement and chaos in the T ¯ T /J ¯ T -deformed CFTs

: In this paper, we regard the T ¯ T / J ¯ T -deformed CFTs as perturbation theories and calculate the first order correction of the correlation functions due to the T ¯ T / J ¯ T - deformation. As applications, we study the R´enyi entanglement entropy of excited state in the T ¯ T / J ¯ T -deformed two-dimensional CFTs. We find, up to the first order perturbation of the deformation, the R´enyi entanglement entropy of locally excited states will acquire a non-trivial time dependence. The excess of the R´enyi 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 -deformations do not change the maximal chaotic behavior of holographic CFTs up to the first order of the deformations.