The BPS correlators of the symmetric product orbifold \text{Sym}_N(\mathbb{T}^4) are reproduced from the dual worldsheet theory describing strings on \text{AdS}_3\times {\rm S}^3\times \mathbb{T}^4 with minimal (k=1) NS-NS flux. More specifically, we show that the worldsheet duals of the symmetric orbifold BPS states can be identified with their lift to the covering surface, thereby making the matching of the correlators essentially manifest. We also argue that the argument can be generalised to arbitrary descendants, using suitable DDF operators on the worldsheet.
