String correlators on $\text{AdS}_3$: Three-point functions

TL;DR

This paper derives a closed-form formula for three-point functions of spectrally flowed string operators on Euclidean AdS3, advancing the understanding of string correlators in curved backgrounds.

Contribution

It provides the first explicit conjecture of a closed formula for three-point functions with arbitrary spectral flow in AdS3 string theory.

Findings

Derived a closed formula for three-point functions with spectral flow

Solved all known constraints of the model

Established fusion rules for the theory

Abstract

We revisit the computation of string worldsheet correlators on Euclidean $\text{AdS}_3$ with pure NS-NS background. We compute correlation functions with insertions of spectrally flowed operators. We explicitly solve all the known constraints of the model and for the first time conjecture a closed formula for three-point functions with arbitrary amount of spectral flow. We explain the relation of our results with previous computations in the literature and derive the fusion rules of the model. This paper is the first in a series with several installments.