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For string theory on AdS$_3$ with pure NS-NS flux a complete set of DDFoperators is constructed, from which one can read off the symmetry algebra ofthe spacetime CFT. Together with an analysis of the spacetime spectrum, thisallows us to show that the CFT dual of superstring theory on ${\rm AdS}_3\times {\rm S}^3 \times \mathbb{T}^4$ for generic NS-NS flux is the symmetricorbifold of $({\cal N}=4$ Liouville theory$)\times \mathbb{T}^4$. For the caseof minimal flux ($k=1$), the Liouville factor disappears, and we just obtainthe symmetric orbifold of $\mathbb{T}^4$, thereby giving further support to aprevious claim. We also show that a similar analysis can be done for bosonicstring theory on ${\rm AdS}_3 \times X$.

String theory on $\boldsymbol{\text{AdS}_{\mathbf{3}}}$ and the symmetric orbifold of Liouville theory