  We study string theory in three-dimensional Anti-de Sitter spacetime in the
path integral formalism. We derive expressions for generic spectrally-flowed
near-boundary vertex operators in the Wakimoto representation, and relate their
correlation functions to covering maps from the worldsheet to the target space
boundary. We show that the path integral structurally reproduces correlation
functions of the dual symmetric orbifold theory. By rephrasing spectral flow as
the introduction of a background gauge field, we provide a path integral
derivation of the localisation property of the near boundary theory. We then
focus on the case of IIB string theory on
$\text{AdS}_3\times\text{S}^3\times\mathbb{T}^4$ with $k=1$ units of NS-NS
flux, where the relationship between correlation functions and covering maps
can be made sharp. We also comment on the relation of the $k=1$ theory and
twistor theory.
