Spectral flow and the exact AdS${}_3\mathrm{/}$CFT${}_2$ chiral ring

We compute all worldsheet three-point functions involving spectrally-flowed operators in chiral multiplets of the space-time theory for strings in AdS${}_3\times$S${}^3\times$T${}^4$, thus completing the analysis of the full AdS${}_3$/CFT${}_2$ chiral ring. We make use of techniques recently developed for the bosonic sector, based on holomorphic covering maps from the worldsheet to the AdS${}_3$ boundary. We highlight the role of the so-called series identifications when dealing with the complications originated by picture-changing spectrally-flowed states. We find an exact agreement with the predictions from the holographic CFT at the symmetric orbifold point, including both extremal and non-extremal correlators.