Holographic Complexity and de Sitter Space

Abstract

We compute the length of spacelike geodesics anchored at opposite sides of certain double-sided flow geometries in two dimensions. These geometries are asymptotically anti-de Sitter but they admit either a de Sitter or a black hole event horizon in the interior. While in the geometries with black hole horizons, the geodesic length always exhibit linear growth at late times, in the flow geometries with de Sitter horizons, geodesics with finite length only exist for short times of the order of the inverse temperature and they do not exhibit linear growth. We comment on the implications of these results towards understanding the holographic proposal for quantum complexity and the holographic nature of the de Sitter horizon.

42 pages

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Cited by in corpus (14)

• Quantum Computational Complexity -- From Quantum Information to Black Holes and Back
• de Sitter Microstates from $T\bar{T}+{\Lambda }_2$ and the Hawking-Page Transition
• The central dogma and cosmological horizons
• Krylov complexity in large-$q$ and double-scaled SYK model
• Cosmological Krylov Complexity
• Holographic Complexity in dS${}_{d+1}$
• Finite Features of Quantum De Sitter Space
• Interpolating geometries and the stretched dS${}_2$ horizon
• An Outsider's Perspective on Information Recovery in de Sitter Space
• Complex geodesics in de Sitter space
• Late-Time Correlators and Complex Geodesics in de Sitter Space
• Multiverse in Karch-Randall Braneworld
• Action complexity of charged black holes with higher derivative interactions
• The semiclassical gravitational path integral and random matrices