de Sitter extremal surfaces

Abstract

We study extremal surfaces in de Sitter space in the Poincare slicing in the upper patch, anchored on spatial subregions at the future boundary ${\mathcal{I}}^{+}$, restricted to constant boundary Euclidean time slices (focussing on strip subregions). We find real extremal surfaces of minimal area as the boundaries of past lightcone wedges of the subregions in question: these are null surfaces with vanishing area. We also find complex extremal surfaces as complex extrema of the area functional, and the area is not always real-valued. In $d{S}_4$ the area is real. The area has structural resemblance with entanglement entropy in a dual $CFT$. There are parallels with analytic continuation from the Ryu-Takayanagi expressions for holographic entanglement entropy in $AdS$. We also discuss extremal surfaces in the $dS$ black brane and the de Sitter "bluewall" studied previously. The $d{S}_4$ black brane complex surfaces exhibit a real finite cutoff-independent extensive piece. In the bluewall geometry, there are real surfaces that go from one asymptotic universe to the other through the Cauchy horizons.

Latex, 21pgs, 2 figs, v3,v4: clarifications added on the wavefunction of the universe; published version

References in corpus (47)

• Holographic Derivation of Entanglement Entropy from AdS/CFT
• Non-Gaussian features of primordial fluctuations in single field inflationary models
• A Stress Tensor for Anti-de Sitter Gravity
• Aspects of Holographic Entanglement Entropy
• Entropy and Area
• A Covariant Holographic Entanglement Entropy Proposal
• Holographic Reconstruction of Spacetime and Renormalization in the AdS/CFT Correspondence
• Lecture Notes on Holographic Renormalization
• Cool horizons for entangled black holes
• The dS/CFT Correspondence
• Generalized gravitational entropy
• Quantum corrections to holographic entanglement entropy
• Holographic Entanglement Entropy: An Overview
• Time Evolution of Entanglement Entropy from Black Hole Interiors
• Reduced density matrices and entanglement entropy in free lattice models
• On the Holographic Renormalization Group
• Entanglement Renyi entropies in holographic theories
• Quantum Gravity In De Sitter Space
• Holographic and Wilsonian Renormalization Groups
• The Black Hole Singularity in AdS/CFT
• Stress Tensors and Casimir Energies in the AdS/CFT Correspondence
• A remark on the AdS/CFT correspondence and the renormalization group flow
• Entanglement Entropy from a Holographic Viewpoint
• Causal Holographic Information
• Entanglement entropy in de Sitter space
• Wilson Lines and Entanglement Entropy in Higher Spin Gravity
• Geometric Holography, the Renormalization Group and the c-Theorem
• De Sitter Musings
• Operator Dictionaries and Wave Functions in AdS/CFT and dS/CFT
• Integrating out geometry: Holographic Wilsonian RG and the membrane paradigm
• The Wave Function of Vasiliev's Universe - A Few Slices Thereof
• Entanglement Entropy and Higher Spin Holography in AdS${}_3$
• State/Operator Correspondence in Higher-Spin dS/CFT
• Entanglement entropy of $\alpha$-vacua in de Sitter space
• Higher Spin Realization of the dS/CFT Correspondence
• Higher Spin de Sitter Holography from Functional Determinants
• Entanglement and out-of-equilibrium dynamics in holographic models of de Sitter QFTs
• Topology of Future Infinity in dS/CFT
• Bi-local Construction of Sp(2N)/dS Higher Spin Correspondence
• AdS plane waves and entanglement entropy
• Entanglement Entropy of de Sitter Space α-Vacua
• de Sitter space and extremal surfaces for spheres
• A paucity of bulk entangling surfaces: AdS wormholes with de Sitter interiors
• Tracing Through Scalar Entanglement
• Complex Entangling Surfaces for AdS and Lifshitz Black Holes?
• Double Trace Flows and Holographic RG in dS/CFT correspondence
• dS/CFT at uniform energy density and a de Sitter "bluewall"

Cited by in corpus (41)

• Surface/State Correspondence as a Generalized Holography
• Pseudo Entropy in dS/CFT and Time-like Entanglement Entropy
• Timelike entanglement entropy
• de Sitter space, extremal surfaces and "time-entanglement"
• The central dogma and cosmological horizons
• Holography in de Sitter Space via Chern-Simons Gauge Theory
• CFT duals of three-dimensional de Sitter gravity
• On holographic time-like entanglement entropy
• Non-local Entanglement and Fast Scrambling in De-Sitter Holography
• Comments on Entanglement Entropy in the dS/CFT Correspondence
• On extremal surfaces and de Sitter entropy
• Wedge Holography in Flat Space and Celestial Holography
• de Sitter space and extremal surfaces for spheres
• On de Sitter future-past extremal surfaces and the "entanglement wedge"
• On $d{S}_4$ extremal surfaces and entanglement entropy in some ghost CFTs
• Logarithmic Corrections, Entanglement Entropy, and UV Cutoffs in de Sitter Spacetime
• Cosmologies, singularities and quantum extremal surfaces
• de Sitter entropy as entanglement
• Ghost-spin chains, entanglement and $bc$-ghost CFTs
• Complex saddles of three-dimensional de Sitter gravity via holography
• Towards a dS/MERA correspondence
• Schwarzschild de Sitter and extremal surfaces
• The Cosmological OTOC: A New Proposal for Quantifying Auto-Correlated Random Non-Chaotic Primordial Fluctuations
• Flat-Space Limit of Holographic Pseudo Entropy in (A)dS Spacetimes
• Holographic entanglement entropies for Schwarzschild and Reisner-Nordström black holes in asymptotically Minkowski spacetimes
• Probing de Sitter Space Using CFT States
• Loschmidt echo, emerging dual unitarity and scaling of generalized temporal entropies after quenches to the critical point
• Emergent $\alpha$-like fermionic vacuum structure and entanglement in the hyperbolic de Sitter spacetime
• Closed FRW holography: A time-dependent ER=EPR realization
• Holographic $T\bar{T}$ deformation of the entanglement entropy in (A)dS${}_3$/CFT${}_2$
• $dS$ extremal surfaces, replicas, boundary Renyi entropies in $dS/CFT$ and time entanglement
• Horizon causality from holographic scattering in asymptotically dS${}_3$
• Entangled spins and ghost-spins
• N-level ghost-spins and entanglement
• Einstein's equations and the pseudo-entropy of pseudo-Riemannian information manifolds
• Holographic timelike entanglement in AdS${}_3$ Vaidya
• Toward a Unified de Sitter Holography: A Composite $T\bar{T}$ and $T\bar{T}+{\Lambda }_2$ Flow
• Holographic de Sitter Spacetime and Quantum Corrections to The Cosmological Constant
• Entangled universes
• On the Spread of Entanglement at Finite Cutoff
• Noncommutative corrections to the minimal surface areas of the pure AdS spacetime and Schwarzschild-AdS black hole