De Sitter entropy as holographic entanglement entropy

TL;DR

This paper reviews how holographic entanglement entropy calculations in spaces with horizons, like de Sitter space, relate to gravitational entropy, including higher-curvature corrections and the role of UV cutoffs.

Contribution

It clarifies the holographic computation of entanglement entropy in de Sitter space and its connection to gravitational and Wald entropy, incorporating higher-curvature effects.

Findings

Entanglement entropy matches de Sitter entropy with logarithmic corrections.

Holographic entanglement entropy can be identified with gravitational entropy when the entangling surface is the horizon.

UV cutoff relates to the effective Planck mass and degrees of freedom of the dual theory.

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.