De Sitter entropy as holographic entanglement entropy

Nikolaos Tetradis

doi:10.21468/scipostphysproc.4.002

Abstract

We review the results of refs. [1,2], in which the entanglement entropy in spaces with horizons, such as Rindler or de Sitter space, is computed using holography. This is achieved through an appropriate slicing of anti-de Sitter space and the implementation of a UV cutoff. When the entangling surface coincides with the horizon of the boundary metric, the entanglement entropy can be identified with the standard gravitational entropy of the space. For this to hold, the effective Newton's constant must be defined appropriately by absorbing the UV cutoff. Conversely, the UV cutoff can be expressed in terms of the effective Planck mass and the number of degrees of freedom of the dual theory. For de Sitter space, the entropy is equal to the Wald entropy for an effective action that includes the higher-curvature terms associated with the conformal anomaly. The entanglement entropy takes the expected form of the de Sitter entropy, including logarithmic corrections.

Highlights

The fact that the divergent part of the entanglement entropy scales with the area of the entangling surface [3, 4] suggests a connection with the gravitational entropy of spaces containing horizons
We address this problem in the context of the AdS/CFT correspondence through use of appropriate coordinates that set the boundary metric in Rindler or static de Sitter form
The corresponding entanglement entropy can obtained through holography by computing the area of the minimal surface γA of ref. [5,6,7]

Summary

Introduction

It seems reasonable that the entropies should become equal when the entangling surface is identified with a horizon. The Rindler horizon at y = 0 corresponds to the point (0, −1) in fig. In global coordinates this surface corresponds to a straight line through the bulk, as depicted by the red line in fig.

Results

Conclusion