de Sitter space and extremal surfaces for spheres

TL;DR

This paper explores extremal surfaces in de Sitter space and their relation to holographic entanglement entropy, revealing universal coefficients linked to conformal anomalies in even dimensions through holographic dualities.

Contribution

It demonstrates the existence of complex extremal surfaces in de Sitter space and connects their properties to conformal anomalies via holographic methods.

Findings

Universal coefficients of logarithmic divergences identified in extremal surface areas.

Agreement between holographic calculations and conformal anomaly coefficients.

Analytic continuation links de Sitter extremal surfaces to AdS holographic entanglement entropy.

Abstract

Following arXiv:1501.03019 [hep-th], we study de Sitter space and spherical subregions on a constant boundary Euclidean time slice of the future boundary in the Poincare slicing. We show that as in that case, complex extremal surfaces exist here as well: for even boundary dimensions, we isolate the universal coefficient of the logarithmically divergent term in the area of these surfaces. There are parallels with analytic continuation of the Ryu-Takayanagi expressions for holographic entanglement entropy in $AdS/CFT$. We then study the free energy of the dual Euclidean CFT on a sphere holographically using the $dS/CFT$ dictionary with a dual de Sitter space in global coordinates, and a classical approximation for the wavefunction of the universe. For even dimensions, we again isolate the coefficient of the logarithmically divergent term which is expected to be related to the conformal anomaly. We find agreement including numerical factors between these coefficients.