  Constructing a holographic string theory dual for a CFT in the perturbative,
weakly coupled regime is a holy grail for gauge/string dualities that would not
only open the door for proofs of the AdS/CFT correspondence but could also
provide novel examples of string duals with and without supersymmetry. In this
work we consider some marginal perturbation of a family of symmetric product
orbifolds in two dimensions. From their correlation functions we engineer a
bosonic string theory whose amplitudes are shown to reproduce the CFT
correlation function order-by-order both in the coupling and in $1/N$. Our
derivation does not require to compute and compare correlation functions
explicitly but rather relies on a sequence of identities that can be derived
using path integral methods. The bosonic string theory we engineer is based on
the field content of the Kac-Wakimoto representation of strings in $AdS_3$ with
$k$ units of pure NSNS flux, but the interaction terms we obtain are different.
They include current algebra preserving interaction terms with one unit of
spectral flow.
