Solving AdS$_3$ string theory at minimal tension: tree-level correlators

TL;DR

This paper introduces a new free-field approach to minimal tension AdS3 string theory, successfully reproducing boundary correlators and clarifying the localization of string amplitudes at tree level.

Contribution

It proposes a novel free-field description of the worldsheet theory and demonstrates how localization arises, enabling explicit calculations of correlators matching boundary CFT results.

Findings

Reproduces the worldsheet partition function of the $rak{psu}(1,1|2)_1$ WZW model

Provides explicit expressions for spectrally-flowed vertex and DDF operators

Achieves a precise tree-level match with boundary symmetric orbifold correlators

Abstract

We revisit the minimal tension ($k=1$) string theory on $\text{AdS}_3\times\text{S}^3\times\mathbb{T}^4$. We propose a new free-field description of the worldsheet theory and show how localization of string amplitudes emerges from the path integral. We exemplify our proposal by reproducing the worldsheet partition function of the $\mathfrak{psu}(1,1|2)_1$ WZW model and providing explicit expressions for spectrally-flowed vertex operators and DDF operators. We compute string correlators in the path integral formalism and obtain a precise tree-level match with correlation functions of the boundary symmetric orbifold.