Effective density matrix for vacua in asymptotically flat gravity

Fuente: arXiv
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Autores principales: He, Temple, Mitra, Prahar, Zurek, Kathryn M.
Formato: Preprint
Publicado: 2025
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author He, Temple
Mitra, Prahar
Zurek, Kathryn M.
author_facet He, Temple
Mitra, Prahar
Zurek, Kathryn M.
contents We explicitly construct the density matrix associated to the vacuum state of a large spherically symmetric causal diamond of area $A$ in four-dimensional asymptotically flat gravity. We achieve this using the soft effective action, which characterizes the low-energy gravitational degrees of freedom that arise in the long-distance limit of the Einstein-Hilbert action and consists of both the soft graviton mode and the Goldstone mode arising from the spontaneous breaking of supertranslation symmetry. Integrating out the soft graviton mode, we obtain an effective action for purely the Goldstone mode, from which we extract the density matrix and therefore the modular Hamiltonian $K_s$ associated to the vacuum state. As a corollary, we explicitly compute the mean and variance of $K_s$, finding $\langle Δ{K}_s^2 \rangle = A/ε_{\text{UV}}^2$, with $ε_{\text{UV}}$ being a length-scale UV cutoff on the celestial sphere.
format Preprint
id arxiv_https___arxiv_org_abs_2509_13401
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Effective density matrix for vacua in asymptotically flat gravity
He, Temple
Mitra, Prahar
Zurek, Kathryn M.
High Energy Physics - Theory
General Relativity and Quantum Cosmology
Quantum Physics
We explicitly construct the density matrix associated to the vacuum state of a large spherically symmetric causal diamond of area $A$ in four-dimensional asymptotically flat gravity. We achieve this using the soft effective action, which characterizes the low-energy gravitational degrees of freedom that arise in the long-distance limit of the Einstein-Hilbert action and consists of both the soft graviton mode and the Goldstone mode arising from the spontaneous breaking of supertranslation symmetry. Integrating out the soft graviton mode, we obtain an effective action for purely the Goldstone mode, from which we extract the density matrix and therefore the modular Hamiltonian $K_s$ associated to the vacuum state. As a corollary, we explicitly compute the mean and variance of $K_s$, finding $\langle Δ{K}_s^2 \rangle = A/ε_{\text{UV}}^2$, with $ε_{\text{UV}}$ being a length-scale UV cutoff on the celestial sphere.
title Effective density matrix for vacua in asymptotically flat gravity
topic High Energy Physics - Theory
General Relativity and Quantum Cosmology
Quantum Physics
url https://arxiv.org/abs/2509.13401