Correlation functions, entanglement and chaos in the TT¯ / JT¯ -deformed CFTs
Song He, Hongfei Shu
Abstract
In this paper, we regard the $T\\bar{T}$/$J\\bar{T}$-deformed CFTs as perturbation theories and compute the first order correction of the correlation functions due to the $T\\bar{T}$/$J\\bar{T}$-deformation. As applications, we study the R\\'enyi entanglement entropy of excited state in the $T\\bar{T}$/$J\\bar{T}$-deformed two-dimensional CFTs. We find, up to the perturbation first order of the deformation, the R\\'enyi entanglement entropy of locally excited state will obtain a nontrivial time dependence. The excess of the R\\'enyi entanglement entropy of locally excited state will also be dramatically changed up to order ${\\cal O}(c)$. Furthermore, we investigate the out of time ordered correlation function to confirm that the $T\\bar{T}$/$J\\bar{T}$-deformations do not change the maximal chaotic behavior of holographic CFTs up to the first order of the deformations.