Quantum Entropy Function from AdS(2)/CFT(1) Correspondence

Abstract

We review and extend recent attempts to find a precise relation between extremal black hole entropy and degeneracy of microstates using AdS_2/CFT_1 correspondence. Our analysis leads to a specific relation between degeneracy of black hole microstates and an appropriately defined partition function of string theory on the near horizon geometry, -- named the quantum entropy function. In the classical limit this reduces to the usual relation between statistical entropy and Wald entropy.Comment: LaTeX file, 27 pages, A modified and extended version of the talk given at Strings 200