On extremal surfaces and de Sitter entropy

TL;DR

This paper investigates extremal surfaces in de Sitter space, revealing connections to de Sitter entropy and proposing a duality with entangled ghost-CFTs, offering new insights into holography in de Sitter space.

Contribution

It identifies extremal timelike surfaces in de Sitter space whose areas relate to de Sitter entropy and explores a potential dS/CFT duality involving entangled ghost-CFTs.

Findings

Connected timelike extremal surfaces stretch from future to past boundary.

Minimal area surfaces have a divergent part proportional to de Sitter entropy.

Entangled ghost-CFT states have positive norm and positive entanglement.

Abstract

We study extremal surfaces in the static patch coordinatization of de Sitter space, focussing on the future and past universes. We find connected timelike codim-2 surfaces on a boundary Euclidean time slice stretching from the future boundary $I^+$ to the past boundary $I^-$. In a limit, these surfaces pass through the bifurcation region and have minimal area with a divergent piece alone, whose coefficient is de Sitter entropy in 4-dimensions. These are reminiscent of rotated versions of certain surfaces in the $AdS$ black hole. We close with some speculations on a possible $dS/CFT$ interpretation of 4-dim de Sitter space as dual to two copies of ghost-CFTs in an entangled state. For a simple toy model of two copies of ghost-spin chains, we argue that similar entangled states always have positive norm and positive entanglement.