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.
