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The bound state of one NS5 brane (wrapped on a $\mathbb{T}^4$) and $N$NS1-branes has two dual descriptions: its low-energy dynamics is described bythe symmetric orbifold of $\mathbb{T}^4$, while the near horizon geometry iscaptured by string theory on ${\rm AdS}_3 \times {\rm S}^3\times \mathbb{T}^4$with one unit of NS flux. The latter theory is exactly solvable in the hybridformalism, and this allows one to prove the equivalence of the twodescriptions. In this paper we extend this duality to $\mathbb{Z}_k$ orbifoldsof this ${\rm AdS}_3 \times {\rm S}^3$ background. In particular, we show thatthe corresponding worldsheet spectrum reproduces exactly the perturbativeexcitations on top of a certain non-perturbative state in the dual symmetricorbifold theory. Since the ${\rm AdS}/{\rm CFT}$ duality map is exact for thesemodels, we obtain an interesting picture of how the duality relates boundaryand bulk descriptions.

Tensionless strings on ${\rm AdS}_3$ orbifolds