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A perturbative CFT dual for pure NS-NS AdS$_3$ strings

We construct a CFT dual to string theory on AdS$_3$ with pure NS-NS flux. It is given by a symmetric orbifold of a linear dilaton theory deformed by a marginal operator from the twist-2 sector. We compute two- and three-point functions on the CFT side to 4th order in conformal perturbation theory at large $N$. They agree with the string computation at genus 0, thus providing ample evidence for a duality. We also show that the full spectra of both short and long strings on the CFT and the string side match. The duality should be understood as perturbative in $N^{-1}$.