No boundary density matrix in elliptic de Sitter dS/${\mathbb{Z}}_2$

Abstract

Elliptic de Sitter (dS) spacetime dS$/{\mathbb{Z}}_2$ is a non-time-orientable spacetime obtained by imposing an antipodal identification to global dS. Unlike QFT on global dS, whose vacuum state can be prepared by a no-boundary Euclidean path integral, the Euclidean elliptic dS does not define a wavefunction in the usual sense. We propose instead that the path integral on the Euclidean elliptic dS defines a no-boundary density matrix. As an explicit example, we study the free Dirac fermion CFT in two-dimensional elliptic dS and analytically compute the von Neumann and the Rényi entropies of this density matrix. The calculation reduces to correlation functions of vertex operators on non-orientable surfaces. As a by-product, we compute the time evolution of entanglement entropy following a crosscap quench in free Dirac fermion CFT. We also comment on a striking feature of free QFT in elliptic dS: its global Hilbert space is one-dimensional, wheres the Hilbert space associated to each observer is a nontrivial Fock space.

28 pages + appendices, 14 figures; v2: matches the published version

References in corpus (26)

• Entanglement Entropy and Quantum Field Theory
• Non-Gaussian features of primordial fluctuations in single field inflationary models
• Evolution of Entanglement Entropy in One-Dimensional Systems
• The dS/CFT Correspondence
• Conformal Vacua and Entropy in de Sitter Space
• Transcending the ensemble: baby universes, spacetime wormholes, and the order and disorder of black hole information
• Entanglement entropy in de Sitter space
• The dS/dS Correspondence
• Holographic Pseudo Entropy
• De Sitter Holography and Entanglement Entropy
• Physics at the entangling surface
• Timelike entanglement entropy
• Elliptic de Sitter Space: dS/Z_2
• de Sitter space, extremal surfaces and "time-entanglement"
• Pseudo Entropy in Free Quantum Field Theories
• Measuring Black Hole Formations by Entanglement Entropy via Coarse-Graining
• Holography in de Sitter Space via Chern-Simons Gauge Theory
• Crosscap States in Integrable Field Theories and Spin Chains
• Closed universes in two dimensional gravity
• Exact Thermal Eigenstates of Nonintegrable Spin Chains at Infinite Temperature
• Holographic Dual of Crosscap Conformal Field Theory
• Thermal Pure States for Systems with Antiunitary Symmetries and Their Tensor Network Representations
• Observers seeing gravitational Hilbert spaces: abstract sources for an abstract path integral
• Tensor network simulations for nonorientable surfaces
• Crosscap states and duality of Ising field theory in two dimensions
• New Crosscap States