Note on higher-point correlation functions of the $T\bar{T}$ or $J\bar{T}$ deformed CFTs

TL;DR

The paper develops a perturbative CFT approach to compute first-order corrections to generic $n$-point functions in $T\bar{T}$ and $J\bar{T}$ deformed CFTs, employing Ward identities to express deformations in terms of cross-ratio functions and conformal data. It then applies these results to the OTOC in the Ising model, showing that late-time growth and integrability properties are preserved at this order for both deformations. The work provides explicit structures for TTbar/JTbar-induced corrections and validates them against known low-point functions, offering a framework to explore quantum chaos and entanglement in irrelevant deformations. Overall, the findings support that TTbar and JTbar deformations maintain substantial undeformed CFT symmetries and integrability in the perturbative regime, with potential implications for replica-based entanglement analyses in these theories.

Abstract

We investigate generic n-point correlation functions of conformal field theories (CFTs), with $T\bar{T}$ and $J\bar{T}$ deformations, in terms of the perturbative CFT approach. We systematically obtain the first order correction to the generic correlation functions of CFTs with $T\bar{T}$ or $J\bar{T}$ deformation. We compute the out-of-time ordered correlation function (OTOC) in the Ising model with $T\bar{T}$ or $J\bar{T}$ deformation, which confirms that these deformations do not change the integrable property up to the first order level.