Effective entropy of quantum fields coupled with gravity
Abstract
Entanglement entropy, or von Neumann entropy, quantifies the amount of uncertainty of a quantum state. For quantum fields in curved space, entanglement entropy of the quantum field theory degrees of freedom is well-defined for a fixed background geometry. In this paper, we propose a generalization of the quantum field theory entanglement entropy by including dynamical gravity. The generalized quantity named effective entropy, and its Renyi entropy generalizations, are defined by analytic continuation of a replica calculation. The replicated theory is defined as a gravitational path integral with multiple copies of the original boundary conditions, with a co-dimension-2 brane at the boundary of region we are studying. We discuss different approaches to define the region in a gauge invariant way, and show that the effective entropy satisfies the quantum extremal surface formula. When the quantum fields carry a significant amount of entanglement, the quantum extremal surface can have a topology transition, after which an entanglement island region appears. Our result generalizes the Hubeny-Rangamani-Takayanagi formula of holographic entropy (with quantum corrections) to general geometries without asymptotic AdS boundary, and provides a more solid framework for addressing problems such as the Page curve of evaporating black holes in asymptotic flat spacetime. We applymore »
- Authors:
-
- Univ. of California, Santa Barbara, CA (United States)
- Stanford Univ., CA (United States)
- Publication Date:
- Research Org.:
- Univ. of California, Oakland, CA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP); e Air Force Office of Scientific Research (AFOSR); National Science Foundation (NSF); Simons Foundation
- OSTI Identifier:
- 1853139
- Grant/Contract Number:
- SC0019380; FA9550-19-1-0360; 1720504; PHY-1748958
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of High Energy Physics (Online)
- Additional Journal Information:
- Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2020; Journal Issue: 10; Journal ID: ISSN 1029-8479
- Publisher:
- Springer Nature
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 79 ASTRONOMY AND ASTROPHYSICS; black holes; models of quantum gravity
Citation Formats
Dong, Xi, Qi, Xiao-Liang, Shangnan, Zhou, and Yang, Zhenbin. Effective entropy of quantum fields coupled with gravity. United States: N. p., 2020.
Web. doi:10.1007/jhep10(2020)052.
Dong, Xi, Qi, Xiao-Liang, Shangnan, Zhou, & Yang, Zhenbin. Effective entropy of quantum fields coupled with gravity. United States. https://doi.org/10.1007/jhep10(2020)052
Dong, Xi, Qi, Xiao-Liang, Shangnan, Zhou, and Yang, Zhenbin. Thu .
"Effective entropy of quantum fields coupled with gravity". United States. https://doi.org/10.1007/jhep10(2020)052. https://www.osti.gov/servlets/purl/1853139.
@article{osti_1853139,
title = {Effective entropy of quantum fields coupled with gravity},
author = {Dong, Xi and Qi, Xiao-Liang and Shangnan, Zhou and Yang, Zhenbin},
abstractNote = {Entanglement entropy, or von Neumann entropy, quantifies the amount of uncertainty of a quantum state. For quantum fields in curved space, entanglement entropy of the quantum field theory degrees of freedom is well-defined for a fixed background geometry. In this paper, we propose a generalization of the quantum field theory entanglement entropy by including dynamical gravity. The generalized quantity named effective entropy, and its Renyi entropy generalizations, are defined by analytic continuation of a replica calculation. The replicated theory is defined as a gravitational path integral with multiple copies of the original boundary conditions, with a co-dimension-2 brane at the boundary of region we are studying. We discuss different approaches to define the region in a gauge invariant way, and show that the effective entropy satisfies the quantum extremal surface formula. When the quantum fields carry a significant amount of entanglement, the quantum extremal surface can have a topology transition, after which an entanglement island region appears. Our result generalizes the Hubeny-Rangamani-Takayanagi formula of holographic entropy (with quantum corrections) to general geometries without asymptotic AdS boundary, and provides a more solid framework for addressing problems such as the Page curve of evaporating black holes in asymptotic flat spacetime. We apply the formula to two example systems, a closed two-dimensional universe and a four-dimensional maximally extended Schwarzchild black hole. We discuss the analog of the effective entropy in random tensor network models, which provides more concrete understanding of quantum information properties in general dynamical geometries. We show that, in absence of a large boundary like in AdS space case, it is essential to introduce ancilla that couples to the original system, in order for correctly characterizing quantum states and correlation functions in the random tensor network. Using the superdensity operator formalism, we study the system with ancilla and show how quantum information in the entanglement island can be reconstructed in a state-dependent and observer-dependent map. We study the closed universe (without spatial boundary) case and discuss how it is related to open universe.},
doi = {10.1007/jhep10(2020)052},
journal = {Journal of High Energy Physics (Online)},
number = 10,
volume = 2020,
place = {United States},
year = {Thu Oct 08 00:00:00 EDT 2020},
month = {Thu Oct 08 00:00:00 EDT 2020}
}
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Works referencing / citing this record:
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