A duality in string theory on AdS3

We consider bosonic string theory on AdS3 supported by Kalb-Ramond flux. It is well known that the α′ exact worldsheet theory is described by the SL(2,R) WZW model. In this note we perform checks of an α′ 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 α′.