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

TL;DR

This work develops a controlled perturbative framework for $T\bar{T}$ and $J\bar{T}$ deformations of two-dimensional CFTs, deriving first-order corrections to 2- and 4-point correlation functions via Ward identities and dimensional regularization. It then applies these results to two physical probes: the Rényi entanglement entropy of locally excited states and the out-of-time-ordered correlator, showing that TTbar and J\bar{T} deformations introduce nontrivial time dependence and UV/IR regulator effects in entanglement growth, while leaving the maximal chaos bound $\lambda_L=2\pi/\beta$ intact at this order. The analysis is performed in the large central charge regime and extended to both deformations, providing explicit expressions for the corrections and highlighting the consistency with holographic expectations. Overall, the paper furnishes a coherent perturbative picture connecting irrelevant deformations to entanglement dynamics and chaos diagnostics in 2D CFTs, with potential tests against nonperturbative results and holographic duals.

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 Rényi 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 Rényi entanglement entropy of locally excited states will acquire a non-trivial time dependence. The excess of the Rényi 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.