Bulk metric reconstruction from boundary entanglement

Roy, Shubho R.; Sarkar, Debajyoti (2018). Bulk metric reconstruction from boundary entanglement. Physical review. D - particles, fields, gravitation, and cosmology, 98(6), 066017. American Physical Society 10.1103/PhysRevD.98.066017

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Most of the literature in the bulk reconstruction program in holography focuses on recovering local bulk operators propagating on a quasilocal bulk geometry and the knowledge of the bulk geometry is always assumed or guessed. The fundamental problem of the bulk reconstruction program, which is recovering the bulk background geometry (metric) from the boundary CFT state is still outstanding. In this work, we formulate a recipe to extract the bulk metric itself from the boundary state, specifically, the modular Hamiltonian information of spherical subregions in the boundary. Our recipe exploits the recent construction of Kabat and Lifschytz [J. High Energy Phys. 06 (2017) 120.] to first compute the bulk two point function of scalar fields directly in the CFT without knowledge of the bulk metric or the equations of motion, and then to take a large scaling dimension limit (WKB) to extract the geodesic distance between two close points in the bulk i.e., the metric. As a proof of principle, we consider three dimensional bulk and selected CFT states such as the vacuum and the thermofield double states. We show that they indeed reproduce the pure AdS and the regions outside the Rindler wedge and the BTZ black hole up to a rigid conformal factor. Since our approach does not rely on symmetry properties of the CFT state, it can be applied to reconstruct asymptotically AdS geometries dual to arbitrary general CFT states provided the modular Hamiltonian is available. We discuss several obvious extensions to the case of higher spacetime dimensions as well as some future applications, in particular, for constructing metric beyond the causal wedge of a boundary region. In the process, we also extend the construction of Kabat and Lifschytz [J. High Energy Phys. 06 (2017) 120.] to incorporate the first order perturbative locality for AdS scalars.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Institute of Theoretical Physics

UniBE Contributor:

Sarkar, Debajyoti

Subjects:

500 Science > 530 Physics

ISSN:

1550-7998

Publisher:

American Physical Society

Language:

English

Submitter:

Esther Fiechter

Date Deposited:

28 Dec 2018 14:29

Last Modified:

05 Dec 2022 15:21

Publisher DOI:

10.1103/PhysRevD.98.066017

ArXiv ID:

1801.07280

BORIS DOI:

10.7892/boris.122144

URI:

https://boris.unibe.ch/id/eprint/122144

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