The Conformal Field Theory on the Horizon of BTZ Black Hole

In three dimensional spacetime with negative cosmology constant, the general relativity can be written as two copies of SO$(2,1)$ Chern-Simons theory. On a manifold with boundary the Chern-Simons theory induces a conformal field theory–WZW theory on the boundary. In this paper, it is show that with suitable boundary condition for BTZ black hole, the WZW theory can reduce to a massless scalar field on the horizon.