# Correlation functions, entanglement and chaos in the $T\bar{T}$/$J\bar{T}$-deformed CFTs

## TL;DR

This paper investigates how $Tar{T}$ and $Jar{T}$ deformations affect correlation functions, entanglement entropy, and chaos in 2D conformal field theories, revealing non-trivial time dependence and preserved chaos at first order.

## Contribution

It provides the first-order perturbative analysis of correlation functions and entanglement entropy in $Tar{T}$/$Jar{T}$-deformed CFTs, and examines chaos preservation.

## Key findings

- Rènyi entanglement entropy gains non-trivial time dependence.
- Deformations significantly alter entanglement entropy for excited states.
- Chaos behavior remains maximal up to first order in deformation.

## Abstract

In this paper, we regard the $T\bar{T}$/$J\bar{T}$-deformed CFTs as perturbation theories and calculate 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 states will acquire a non-trivial 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, the out of time ordered correlation function is investigated 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.