String correlators on AdS₃: Analytic structure and dual CFT

We continue our study of string correlators on Euclidean AdS₃ AdS 3 with pure NS-NS flux. The worldsheet and spacetime correlators have a rich analytic structure, which we analyse completely for genus 0 four-point functions. We show that correlators exhibit a simple behaviour near their singularities. The spacetime correlators are meromorphic functions in the SL (2, R) S L (2, ℝ) -spins, whose pole structure is shown to agree with the prediction of a recent proposal for the dual CFT₂ CFT 2. Moreover, we also compute the residues of the spacetime correlators for some of the poles exactly and find again a perfect match with the proposal for the dual CFT₂ CFT 2, thereby checking the duality for some non-trivial four-point functions exactly. Our computations simplify drastically in the tensionless limit of AdS₃ S³ T⁴ A d S 3 × S 3 × 𝕋 4 where the behaviour near the poles gives in fact the exact answer. This paper is the third in a series with several installments.