  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.
