A proof for string three-point functions in AdS${}_3$

Abstract

Correlation functions of the $\text{SL}(2,\mathbb{R})$-WZW model involving spectrally flowed vertex operators are notoriously difficult to compute. An explicit integral expression for the corresponding three-point functions was recently conjectured in [arXiv:2105.12130v2]. In this paper, we provide a proof for this conjecture. For this, we extend the methods of [arXiv:2208.00978] based on the so-called $\text{SL}(2,\mathbb{R})$ series identifications, which relate vertex operators belonging to different spectral flow sectors. We also highlight the role of holomorphic covering maps in this context. Our results constitute an important milestone for proving this instance of the AdS${}_3$/CFT${}_2$ holographic duality at finite 't Hooft coupling.

arXiv comment22 pages

References in corpus (22)

• Structure Constants and Conformal Bootstrap in Liouville Field Theory
• Strings in AdS_3 and the SL(2,R) WZW Model. Part 1: The Spectrum
• Strings in AdS_3 and the SL(2,R) WZW Model. Part 2: Euclidean Black Hole
• More Comments on String Theory on AdS_3
• The Worldsheet Dual of the Symmetric Product CFT
• Correlation functions for M^N/S_N orbifolds
• Deriving the ${\text{AdS}}_3/{\text{CFT}}_2$ Correspondence
• Operator product expansion and factorization in the $H_3^{+}$-WZNW model
• Tensionless String Spectra on ${\mathrm{AdS}}_3$
• Superstrings on AdS3 at k=1
• Worldsheet correlators in AdS(3)/CFT(2)
• A perturbative CFT dual for pure NS-NS AdS${}_3$ strings
• Spectral Flow in AdS(3)/CFT(2)
• String correlators on ${\text{AdS}}_3$: Three-point functions
• String Theory of Supertubes
• Little Strings, Long Strings, and Fuzzballs
• Stringy Structure at the BPS Bound
• String dynamics in NS5-F1-P geometries
• Black hole microstates from the worldsheet
• Worldsheet Correlators in Black Hole Microstates
• More AdS_3 correlators
• On spectrally flowed local vertex operators in AdS${}_3$

Cited by in corpus (2)

• Gromov-Witten/Hilbert versus AdS3/CFT2 Correspondence
• Lecture notes on strings in AdS${}_3$ from the worldsheet and the AdS${}_3$/CFT${}_2$ duality