It was recently shown in arXiv:2009.11306 that tree-level correlation functions in tensionless string theory on \rm{AdS}_3\times\rm{S}^3\times\mathbb{T}^4 match the expected form of correlation functions in the symmetric orbifold CFT on \mathbb{T}^4 in the large N limit. This analysis utilized the free-field realization of the \mathfrak{psu}(1,1|2)_1 Wess-Zumino-Witten model, along with a surprising identity directly relating these correlation functions to a branched covering of the boundary of \rm{AdS}_3. In particular, this identity implied the unusual feature that the string theory correlators localize to points in the moduli space for which the worldsheet covers the boundary of \rm{AdS}_3 with specified branching near the insertion points. In this work we generalize this analysis past the tree-level approximation, demonstrating its validity to higher genus worldsheets, and in turn providing strong evidence for this incarnation of the \rm{AdS}/\rm{CFT} correspondence at all orders in perturbation theory.
