de Sitter space and extremal surfaces for spheres

Understand

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.