Correlation Functions in the TsT/$T{\bar T}$ Correspondence

TL;DR

This paper provides a non-perturbative calculation of two-point correlation functions in the TsT/$Tar T$ holographic duality, demonstrating consistency with $Tar T$ deformations and supporting the conjectured correspondence.

Contribution

It offers the first non-perturbative computation of correlation functions in the TsT/$Tar T$ duality, confirming the theoretical predictions and matching with conformal perturbation results.

Findings

Correlation functions match between string theory and $Tar T$ deformed CFT.

Deformed correlators follow a specific momentum-dependent shift in conformal weight.

Results satisfy the Callan-Symanzik equation for $Tar T$ deformations.

Abstract

We investigate the proposed holographic duality between the TsT transformation of IIB string theory on AdS$_3\times {\cal N}$ with NS-NS flux and a single-trace $T\bar{T}$ deformation of the symmetric orbifold CFT. We present a non-perturbative calculation of two-point correlation functions using string theory and demonstrate their consistency with those of the $T\bar{T}$ deformation. The two-point correlation function of the deformed theory on the plane, written in momentum space, is obtained from that of the undeformed theory by replacing $h$ with $h+2{\tilde \lambda\over w} p\bar p$, where $h$ is the spacetime conformal weight, $\tilde \lambda$ is a deformation parameter, $p$ and $\bar p$ are the momenta, and $w$ labels the twisted sectors in the deformed symmetric product. At $w=1$, the non-perturbative result satisfies the Callan-Symanzik equation for double-trace $T\bar T$ deformed CFT derived in \cite{Cardy:2019qao}. We also perform conformal perturbations on both the worldsheet CFT and the symmetric orbifold CFT as a sanity check. The perturbative and non-perturbative matching between results on the two sides provides further evidence of the conjectured TsT/$T\bar{T}$ correspondence.