Horizon causality from holographic scattering in asymptotically dS${}_3$

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.

47 pages, 14 figures, v2: Some modifications including a clarification about the connected wedge theorem and holographic entanglement entropy prescription, v3: Published version in JHEP

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