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

TL;DR

Sen develops a concrete framework tying extremal black hole entropy to microscopic degeneracies via $AdS_2/CFT_1$, defining a quantum entropy function as the finite part of the string partition function on the near-horizon geometry $AdS_2\times K$. The approach unifies macroscopic near-horizon gravity with microscopic brane dynamics, showing that in the classical limit $S_{BH}=S_{micro}$ through Wald entropy and that the finite $AdS_2$ partition function encodes degeneracies $d_{micro}(\vec{q})$. It further relates to the OSV conjecture through F-term contributions, while carefully addressing boundary conditions and non-normalizable modes that affect the precise definition of $Z_{AdS_2}$. The work clarifies how quantum corrections shape entropy counting and highlights caveats and open questions, including the role of single-centered versus multi-centered configurations and potential entanglement-based interpretations.

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.