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

Fuente: arXiv
Salvato in:
Dettagli Bibliografici
Autori principali: Dulac, Raphaël, Wei, Zixia
Natura: Preprint
Pubblicazione: 2025
Soggetti:
Accesso online:
Tags: Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
_version_ 1866909020762144768
author Dulac, Raphaël
Wei, Zixia
author_facet Dulac, Raphaël
Wei, Zixia
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2512_00704
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle No boundary density matrix in elliptic de Sitter dS/$\mathbb{Z}_2$
Dulac, Raphaël
Wei, Zixia
High Energy Physics - Theory
Statistical Mechanics
General Relativity and Quantum Cosmology
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.
title No boundary density matrix in elliptic de Sitter dS/$\mathbb{Z}_2$
topic High Energy Physics - Theory
Statistical Mechanics
General Relativity and Quantum Cosmology
url https://arxiv.org/abs/2512.00704