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

TL;DR

This paper analyzes the analytic structure of string correlators on Euclidean AdS3 with NS-NS flux, confirming dual CFT predictions and providing exact results in the tensionless limit.

Contribution

It provides a complete analysis of genus 0 four-point functions, matching spacetime correlator poles with dual CFT predictions and simplifying results in the tensionless limit.

Findings

Correlators exhibit simple behavior near singularities.

Pole structures match dual CFT predictions.

Exact residues computed in the tensionless limit.

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.