Quantum entropy function from AdS₂/CFT₁ correspondence

Abstract

We review and extend recent attempts to find a precise relation between extremal black hole entropy and degeneracy of microstates using AdS₂/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.