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

Abstract

We investigate the proposed holographic duality between the TsT transformation of IIB string theory on AdS${}_3\times \mathcal{N}$ 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 $h+2\frac{\tilde{\lambda }}{w}p\bar{p}$, 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.

35 pages; references added