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

TL;DR

This paper connects the entropy function formalism for extremal black holes with the AdS(2)/CFT(1) correspondence, expressing black hole entropy as the logarithm of the dual quantum system's ground state degeneracy, and clarifies its relation to Euclidean methods.

Contribution

It introduces a formulation that relates the entropy function to the ground state degeneracy in the dual quantum system, enhancing understanding of quantum black hole entropy.

Findings

Entropy expressed as the logarithm of ground state degeneracy.

Clarification of the relationship between entropy function and Euclidean action formalisms.

Provides a quantum interpretation of extremal black hole entropy.

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.