DDF operators in the Hybrid Formalism

String theory with one unit of NS-NS flux on $\text{AdS}_3 \times \text{S}^3 \times \mathbb{T}^4$ has been recently realised to be the exact dual of the symmetric orbifold of $\mathbb{T}^4$. In the hybrid formalism of Berkovits, Vafa and Witten and using the free-field realisation of $\mathfrak{psu}(1,1|2)_1$, the DDF operators of the free bosons and the free fermions of $\mathbb{T}^4$ are constructed. It is shown that these DDF operators reproduce the whole spectrum of the space-time theory on the world-sheet and therefore provide a derivation of the dual spectrum from first-principles.