Exact Operator Quantization of the Euclidean Black Hole CFT

We present an exact operator quantization of the Euclidean Black Hole CFT using a recently established free field parametrization of the fundamental fields of the classical theory [4, 5, 6, 7]. Quantizing the map to free fields, we show that the resulting quantum fields are causal and transform as covariant fields w.r.t. the Virasoro algebra. We construct the reflection operator of the quantum theory and demonstrate its unitarity. We furthermore discuss the W-algebra of the Euclidean Black Hole model. It turns out that unitarity of the reflection operator is a simple consequence of the fact that certain representations of the W-algebra are unitarily equivalent.