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.
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