Horizon causality from holographic scattering in asymptotically dS$_3$

TL;DR

This paper explores the relationship between bulk scattering processes and boundary causality in asymptotically dS$_3$ spacetime, proposing a connection between static patch holography and the dS/CFT correspondence.

Contribution

It extends the connected wedge theorem to asymptotically dS$_3$ and demonstrates causality consistency in static patch holography.

Findings

Causality on the horizon aligns with boundary null infinities.

Signals in the static patch relate to local operators at infinity.

Suggests a link between static patch holography and dS/CFT.

Abstract

In the AdS/CFT correspondence, a direct scattering in the bulk may not have a local boundary analog. A nonlocal implementation on the boundary requires $O(1/G_N)$ mutual information. This statement is formalized by the connected wedge theorem, which can be proven using general relativity within AdS$_3$ but also argued for using quantum information theory on the boundary, suggesting that the theorem applies to any holographic duality. We examine scattering within the static patch of asymptotically dS$_3$ spacetime, which is conjectured to be described by a quantum theory on the stretched horizon in static patch holography. We show that causality on the horizon induced from null infinities $\mathcal{I}^{\pm}$ is consistent with the theorem. Specifically, signals propagating in the static patch are associated with local operators at $\mathcal{I}^{\pm}$. Our results suggest a novel connection between static patch holography and the dS/CFT correspondence.