  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.
