QUANTUM ENTROPY FUNCTION FROM AdS2/CFT1 CORRESPONDENCE

We review and extend recent attempts to find a precise relation between extremal black hole entropy and degeneracy of microstates using AdS(2)=CFT1 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.