AdS₃ Black Hole Entropy and the Spectral Flow on the Horizon

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We consider the entropy problem of AdS₃ black holes using the conformal field theory at the horizon. We observe that the supersymmetry is enhanced at the horizon of massless AdS₃ black hole. This allows us to determine the vacuum of the modular invariant conformal field theory to be the NS-ground state (which corresponds to AdS₃ spacetime). This is smoothly related to the R-ground state (corresponding to massless black hole) by a spectral flow, which can be understood as a superconformal transformation.