A String Theoretic Derivation of Gibbons-Hawking Entropy

TL;DR

This paper explores a string theory approach to derive Gibbons-Hawking entropy, linking open string species on D-branes to the entropy associated with de Sitter horizons, offering new insights into the area law.

Contribution

It provides a novel string theoretic derivation of Gibbons-Hawking entropy using open-closed correspondence and D-branes, despite the absence of a de Sitter vacuum in string theory.

Findings

Gibbons-Hawking entropy can be derived from open string species on D-branes.

The derivation reveals a critical 't Hooft coupling where the entropy saturates the area law.

The approach offers new understanding of the origin of the area-form in de Sitter space.

Abstract

We describe an attempt of string theoretic derivation of the Gibbons-Hawking entropy. Despite not admitting a de Sitter vacuum, the string theory, by the power of open-close correspondence, captures the Gibbons-Hawking entropy as the entropy of Chan-Paton species on a de Sitter-like state obtained via $D$-branes. Moreover, this derivation sheds a new light at the origin of the area-form, since the equality takes place for a critical 't Hooft coupling for which the species entropy of open strings saturates the area-law unitarity bound.