Holographic entanglement entropy of de Sitter braneworld

TL;DR

This paper investigates the holographic entanglement entropy in a de Sitter braneworld embedded in AdS space, demonstrating its equivalence with de Sitter horizon entropy and Euclidean path integral calculations across dimensions.

Contribution

It provides a detailed comparison showing the equivalence of holographic entanglement entropy with other de Sitter entropies in braneworld models, including cases with Gauss-Bonnet corrections.

Findings

Holographic entanglement entropy matches de Sitter horizon entropy in certain limits.

Euclidean path integral entropy agrees with holographic entropy across dimensions.

Results extend to models with Gauss-Bonnet terms in the bulk.

Abstract

We study the holographic representation of the entanglement entropy, recently proposed by Ryu and Takayanagi, in a braneworld context. The holographic entanglement entropy of a de Sitter brane embedded in an anti-de Sitter (AdS) spacetime is evaluated using geometric quantities, and it is compared with two kinds of de Sitter entropy: a quarter of the area of the cosmological horizon on the brane and entropy calculated from the Euclidean path integral. We show that the three entropies coincide with each other in a certain limit. Remarkably, the entropy obtained from the Euclidean path integral is in precise agreement with the holographic entanglement entropy in all dimensions. We also comment on the case of a five-dimensional braneworld model with the Gauss-Bonnet term in the bulk.