Holographic entanglement entropy of de Sitter braneworld

TL;DR

This work investigates holographic entanglement entropy on a $n$-dimensional de Sitter brane embedded in $(n+1)$-dimensional AdS space, using the Ryu–Takayanagi proposal to compute $S_{ent} = A_{n-1}/(4G_{n+1})$ from a bulk minimal surface anchored on the brane horizon. It demonstrates that $S_{ent}$ exactly matches the brane entropy $S_E$ obtained from the Euclidean path integral across dimensions, and that all three entropies converge to the standard de Sitter horizon entropy $S_{area}$ in the limit $r_0/l \gg 1$, where brane gravity decouples from the bulk. The analysis also reveals that $S_{ent}$ generally differs from $S_{area}$ due to higher-derivative (KK) corrections on the brane. When bulk gravity includes Gauss-Bonnet corrections, a factor $(1+\beta)$ appears in $S_E$ but not in $S_{ent}$, indicating the naive RT prescription requires modification for higher-curvature theories. The results motivate extensions to FRW braneworlds and highlight the boundaries of holographic entropy concepts in braneworld settings.

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.