Solving AdS${}_3$ string theory at minimal tension: tree-level correlators

We revisit the minimal tension ($k=1$) string theory on ${\text{AdS}}_3\times {\text{S}}^3\times {\mathbb{T}}^4$. We propose a new free-field description of the worldsheet theory and show how localization of string amplitudes emerges from the path integral. We exemplify our proposal by reproducing the worldsheet partition function of the $\mathfrak{p}\mathfrak{s}\mathfrak{u}(1,1\mathrm{\mid }2{)}_1$ WZW model and providing explicit expressions for spectrally-flowed vertex operators and DDF operators. We compute string correlators in the path integral formalism and obtain a precise tree-level match with correlation functions of the boundary symmetric orbifold.