A note on the bulk interpretation of the quantum extremal surface formula

Journal article

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 [1], 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 that transform under the quantum group ${{\text{SL}}}_{q}^{+}\left(2,{\mathbb{R}}\right)$ 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.

Authors: Wong, G

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Springer Nature
• Journal: Journal of High Energy Physics
• Volume: 2024
• Issue: 4
• Article number: 24
• Publication date: 2024-04-04
• Acceptance date: 2024-03-11
• DOI: 10.1007/jhep04(2024)024
• EISSN: 1029-8479
• ISSN: 1126-6708
• Language: English
• Keywords: topological field theories; anyons; quantum groups; AdS-CFT correspondence