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

Dei, Andrea; Eberhardt, Lorenz

doi:10.21468/SciPostPhys.13.3.053

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

Abstract

We continue our study of string correlators on Euclidean \text{AdS}_3 ${AdS}_{3}$ 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}) $S L (2, ℝ)$ -spins, whose pole structure is shown to agree with the prediction of a recent proposal for the dual \text{CFT}_2 ${CFT}_{2}$ . 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 ${CFT}_{2}$ , 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 ${A d S}_{3} \times S^{3} \times 𝕋^{4}$ where the behaviour near the poles gives in fact the exact answer. This paper is the third in a series with several installments.

Authors:

Dei, Andrea ^[1]; Eberhardt, Lorenz ^[2]

Harvard University
Institute for Advanced Study

Publication Date:: Tue Sep 06 00:00:00 EDT 2022

Research Org.:: Institute for Advanced Study, Princeton, NJ (United States)

Sponsoring Org.:: USDOE Office of Science (SC)

OSTI Identifier:: 1885621

Alternate Identifier(s):: OSTI ID: 1898409

Grant/Contract Number:: SC0009988

Resource Type:: Published Article

Journal Name:: SciPost Physics

Additional Journal Information:: Journal Name: SciPost Physics Journal Volume: 13 Journal Issue: 3; Journal ID: ISSN 2542-4653

Publisher:: Stichting SciPost

Country of Publication:: Netherlands

Language:: English

Subject:: 74 ATOMIC AND MOLECULAR PHYSICS

Citation Formats


                    Dei, Andrea, and Eberhardt, Lorenz. String correlators on $\text{AdS}_3$: Analytic structure and dual CFT.  Netherlands: N. p., 2022. 
Web.  doi:10.21468/SciPostPhys.13.3.053.

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                    Dei, Andrea, & Eberhardt, Lorenz. String correlators on $\text{AdS}_3$: Analytic structure and dual CFT.  Netherlands.  https://doi.org/10.21468/SciPostPhys.13.3.053

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                    Dei, Andrea, and Eberhardt, Lorenz. Tue .  
"String correlators on $\text{AdS}_3$: Analytic structure and dual CFT".  Netherlands.  https://doi.org/10.21468/SciPostPhys.13.3.053.

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@article{osti_1885621,

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

  author       = {Dei, Andrea and Eberhardt, Lorenz},

  abstractNote = {We continue our study of string correlators on Euclidean \text{AdS}_3 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}) S L ( 2 , ℝ ) -spins, whose pole structure is shown to agree with the prediction of a recent proposal for the dual \text{CFT}_2 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 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 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.},

  doi          = {10.21468/SciPostPhys.13.3.053},

  journal      = {SciPost Physics},

  number       = 3,

  volume       = 13,

  place        = {Netherlands},

  year         = {Tue Sep 06 00:00:00 EDT 2022},

  month        = {Tue Sep 06 00:00:00 EDT 2022}

}

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