A duality in string theory on AdS$_3$

TL;DR

This paper investigates a proposed duality in bosonic string theory on AdS3, demonstrating the equivalence of vertex operators and correlation functions between two descriptions, revealing a strong-weak duality in the theory.

Contribution

It provides explicit mappings of vertex operators and confirms the duality by matching correlation functions, advancing understanding of string dualities on AdS3.

Findings

Explicit vertex operator map established

Correlation functions shown to be equivalent

Duality confirmed as strong-weak in '

Abstract

We consider bosonic string theory on $\text{AdS}_3$ supported by Kalb-Ramond flux. It is well known that the $\alpha'$ exact worldsheet theory is described by the $\text{SL(2,R)}$ WZW model. In this note we perform checks of an $\alpha'$ exact dual description proposed in [arXiv:2104.07233] involving a winding condensate on a free theory background. We give the explicit map of vertex operators for normalizable states on both sides of the duality and demonstrate the equivalence of their two and three point functions by direct computation. The duality is of strong-weak nature in $\alpha'$.