String correlators on ${\text{AdS}}_3$: Analytic structure and dual CFT

Abstract

We continue our study of string correlators on Euclidean ${\text{AdS}}_3$ 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 $\mathrm{SL}(2,\mathbb{R})$-spins, whose pole structure is shown to agree with the prediction of a recent proposal for the dual ${\text{CFT}}_2$. 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 ${\text{CFT}}_2$, thereby checking the duality for some non-trivial four-point functions exactly. Our computations simplify drastically in the tensionless limit of ${\mathrm{AdS}}_3\times {\mathrm{S}}^3\times {\mathbb{T}}^4$ where the behaviour near the poles gives in fact the exact answer. This paper is the third in a series with several installments.

33 pages

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Cited by in corpus (8)

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• BPS Correlators for ${\text{AdS}}_3/{\text{CFT}}_2$
• Symmetries and Covering Maps for the Minimal Tension String on $\mathbf{Ad}{\mathbf{S}}_3\times {\mathbf{S}}^3\times {\mathbf{T}}^4$
• On spectrally flowed local vertex operators in AdS${}_3$
• A localising AdS${}_3$ sigma model
• Holographic Weyl anomaly in string theory
• Gromov-Witten/Hilbert versus AdS3/CFT2 Correspondence
• Lecture notes on strings in AdS${}_3$ from the worldsheet and the AdS${}_3$/CFT${}_2$ duality