Horizon quantization and thermodynamics of the 2+1 black hole

We test on the 2+1 dimensional black hole the quantization method that we have previously proposed in four dimensions. While in the latter case the horizon dynamics is described, at the effective level, by the action of a relativistic membrane, in the 2+1 case it is described by a string. We show that this approach reproduces the correct value of the temperature and entropy of the 2+1 dimensional black hole, and we write down the Schroedinger equation satisfied by the horizon wave function.