Entropy Function and AdS(2)/CFT(1) Correspondence

TL;DR

The entropy computed in Wald's formula is manipulated this way to express it as the logarithm of the ground state degeneracy of a dual quantum mechanical system, providing a natural definition of the extremal black hole entropy in the full quantum theory.

Abstract

Wald's formula for black hole entropy, applied to extremal black holes, leads to the entropy function formalism. We manipulate the entropy computed this way to express it as the logarithm of the ground state degeneracy of a dual quantum mechanical system. This provides a natural definition of the extremal black hole entropy in the full quantum theory. Our analysis also clarifies the relationship between the entropy function formalism and the Euclidean action formalism.