Entanglement Interpretation of Black Hole Entropy in String Theory

TL;DR

This paper explores how black hole entropy in string theory can be understood as arising from quantum entanglement, using dual field theories and the Hartle-Hawking state, with a detailed example in five-dimensional anti-de Sitter space.

Contribution

It demonstrates that black hole entropy can be interpreted as entanglement entropy within the framework of string theory and dual field theories, providing a new perspective on black hole thermodynamics.

Findings

Entanglement entropy matches black hole entropy in the dual field theory.

The Hartle-Hawking state is shown to be an entangled thermofield double state.

Explicit analysis of five-dimensional anti-de Sitter black hole supports the interpretation.

Abstract

We show that the entropy resulting from the counting of microstates of non extremal black holes using field theory duals of string theories can be interpreted as arising from entanglement. The conditions for making such an interpretation consistent are discussed. First, we interpret the entropy (and thermodynamics) of spacetimes with non degenerate, bifurcating Killing horizons as arising from entanglement. We use a path integral method to define the Hartle-Hawking vacuum state in such spacetimes and discuss explicitly its entangled nature and its relation to the geometry. If string theory on such spacetimes has a field theory dual, then, in the low-energy, weak coupling limit, the field theory state that is dual to the Hartle-Hawking state is a thermofield double state. This allows the comparison of the entanglement entropy with the entropy of the field theory dual, and thus, with the Bekenstein-Hawking entropy of the black hole. As an example, we discuss in detail the case of the five dimensional anti-de Sitter, black hole spacetime.