Statistical entropy and AdS-CFT correspondence in BTZ black holes

We study the AdS-CFT correspondence in the case of AdS₃. We obtain the statistical entropy of the BTZ black hole in terms of the correct central charge and the conformal dimensions for the states corresponding to the BTZ black hole. We point out the difference between our method and the old fashioned approaches based on the SL(2,R) Wess-Zumino-Witten model or Liouville theory.