Correlation functions, entanglement and chaos in the TT/JT-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 Tdeformation. 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 nontrivial 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.