Non-local Entanglement and Fast Scrambling in De-Sitter Holography

TL;DR

This work investigates holographic entanglement and information scrambling in de-Sitter space using the DS/dS correspondence. By extending the exact non-local entanglement structure beyond the time-reflection slice and formulating a two-sided geometry, it analyzes shock-wave-induced traversable wormholes and two-sided OTOCs. The results show that de-Sitter holography realizes fast scrambling with scrambling times saturating the Sekino–Susskind bound, while the late-time two-sided OTOC reaches the Maldacena–Shenker–Stanford chaos bound with a sign dictated by non-local entanglement, offering an ER=EPR interpretation. Together, these findings support a maximally chaotic, teleporation-capable dS quantum gravity framework within the DS/dS setup.

Abstract

We study holographic entanglement and information scrambling in de-Sitter (dS) space in the context of the DS/dS correspondence. We find that our previously identified non-local entanglement structure of dS vacua can be extended out of the time-reflection symmetric slice. We extend the geometry to a two-sided configuration and calculate the zero-time mutual information between two intervals on different sides when there is a localized shock wave in the bulk. Interestingly, we find that the information scrambling time saturates the fast scrambler bound proposed by Sekino and Susskind and that the shock wave renders a wormhole to be traversable. Furthermore, we calculate a two-sided out-of-time-ordered correlator (OTOC) in the late time regime and we see that, before scrambling, it exponentially grows with an exponent whose value saturates the maximal bound of chaos proposed by Maldacena, Shenker and Stanford. At the end, we provide an explanation why the exponential growing of the late-time OTOC with the maximal bound of chaos saturated and the traversability of the wormhole are simple results of the non-local entanglement structure and point out that this is a realization of the ER=EPR proposal.

Figures (10)

• Figure 1: Embedding de-Sitter to a Higher Dimensional Minkowski.
• Figure 2: The Penrose diagram of de-Sitter. Global coordinate covers the whole square and the extended static coordinate only covers regions III and IV. The blue slice is a constant time slice in static coordinate. Each point on the diagram is a $D-2$ sphere.
• Figure 3: The Penrose Diagram of de-Sitter global patch sliced de-Sitter. The solid red slice is a constant $\tau_{d}$ slice and the dashed red slice is $\tau_{d}=0$ slice. The solid green slice is a constant $r$ (radial) slice and the dashed green slice is the $r=\frac{\pi}{2}$ (central) slice. Each point on the diagram is a (D-2)-sphere.
• Figure 4: The Penrose Diagram of de-Sitter extended static patch sliced de-Sitter. To show the difference with de-Sitter global patch sliced de-Sitter, we draw it as two copies of the original diagram and the two edges on the left and right should be identified. Now each point represents a (D-2)-hemisphere. The left panel represents those with $\beta_{d}\in[0,\pi/2]$ and the right one represents those with $\beta_{d}\in[\pi/2,\pi]$. The blue slice represents a constant $t_{d}$ slice where the change of direction in global conformal time T can be seen from Equ.\ref{['eq:transformation2']}.
• Figure 5: The Penrose Diagram of a (D-1)-dimensional de-Sitter (dS) where the field theory system is living on. A constant static time $t_{d}$ slice is shown in blue. Wedges with the same color are antipodally entangled at any constant-time slices. In order to show the non-local nature of the entanglement we draw two panels and each point of the diagram is a (D-3)-hemisphere.