Statistical Entropy and AdS/CFT Correspondence in BTZ Black Holes

TL;DR

This paper explores the AdS/CFT correspondence for BTZ black holes in AdS3, calculating their statistical entropy using conformal field theory techniques and highlighting differences from traditional methods.

Contribution

It introduces a novel approach to compute BTZ black hole entropy via conformal dimensions and central charge, contrasting with older SL(2,R) WZW and Liouville methods.

Findings

Successfully derived the BTZ black hole entropy using CFT data.

Identified key differences between the new method and traditional approaches.

Clarified the role of conformal dimensions in black hole entropy calculation.

Abstract

We study 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 SL(2,R) Wess-Zumino-Witten model or Liouville theory.