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 $\mathfrak{p}\mathfrak{s}\mathfrak{u}(1,1\mathrm{\mid }2{)}_1$, 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.