No boundary density matrix in elliptic de Sitter dS/$\mathbb{Z}_2$
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909020762144768 |
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| 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 |