Double winding condensate CFT

We conjecture a two-dimensional conformal field theory built out of a linear dilaton and a compact $\beta \gamma$ system deformed by winding condensates on each of the compact cycles. In particular, explicit expressions of the residues of the correlation functions are provided. As a worldsheet theory, it describes a stringy black hole in AdS${}_3$ (supported by the Kalb-Ramond flux) at the Hawking-Page temperature. It is expected to be connected to the Horowitz-Polchinski-like solution near the Hagedorn temperature of thermal AdS${}_3$ and Euclidean BTZ blackhole as we vary the temperature.