Saved in:
Bibliographic Details
Main Author: Wong, Gabriel
Format: Preprint
Published: 2022
Subjects:
Online Access:https://arxiv.org/abs/2212.03193
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866910751555321856
author Wong, Gabriel
author_facet Wong, Gabriel
contents Defining quantum information quantities directly in bulk quantum gravity is a difficult problem due to the fluctuations of spacetime. Some progress was made recently in \cite{Mertens:2022ujr}, which provided a bulk interpretation of the Bekenstein Hawking formula for two sided BTZ black holes in terms of the entanglement entropy of gravitational edge modes. We generalize those results to give a bulk entanglement entropy interpretation of the quantum extremal surface formula in AdS3 gravity, as applied to a single interval in the boundary theory. Our computation further supports the proposal that AdS3 gravity can be viewed as a topological phase in which the bulk gravity edge modes are anyons transforming under the quantum group $\SL^{+}_{q}(2,\mathbb{R})$. These edge modes appear when we cut open the Euclidean path integral along bulk co-dimension 2 slices, and satisfies a shrinkable boundary condition which ensures that the Gibbons-Hawking calculation gives the correct state counting.
format Preprint
id arxiv_https___arxiv_org_abs_2212_03193
institution arXiv
publishDate 2022
record_format arxiv
spellingShingle A note on the bulk interpretation of the Quantum Extremal Surface formula
Wong, Gabriel
High Energy Physics - Theory
General Relativity and Quantum Cosmology
Mathematical Physics
Defining quantum information quantities directly in bulk quantum gravity is a difficult problem due to the fluctuations of spacetime. Some progress was made recently in \cite{Mertens:2022ujr}, which provided a bulk interpretation of the Bekenstein Hawking formula for two sided BTZ black holes in terms of the entanglement entropy of gravitational edge modes. We generalize those results to give a bulk entanglement entropy interpretation of the quantum extremal surface formula in AdS3 gravity, as applied to a single interval in the boundary theory. Our computation further supports the proposal that AdS3 gravity can be viewed as a topological phase in which the bulk gravity edge modes are anyons transforming under the quantum group $\SL^{+}_{q}(2,\mathbb{R})$. These edge modes appear when we cut open the Euclidean path integral along bulk co-dimension 2 slices, and satisfies a shrinkable boundary condition which ensures that the Gibbons-Hawking calculation gives the correct state counting.
title A note on the bulk interpretation of the Quantum Extremal Surface formula
topic High Energy Physics - Theory
General Relativity and Quantum Cosmology
Mathematical Physics
url https://arxiv.org/abs/2212.03193