Nonlinear gravity from entanglement in conformal field theories
Nonlinear gravity from entanglement in conformal field theories
In this paper, we demonstrate the emergence of nonlinear gravitational equations directly from the physics of a broad class of conformal field theories. We consider CFT excited states defined by adding sources for scalar primary or stress tensor operators to the Euclidean path integral defining the vacuum state. For these states, we show that up to second order in the sources, the entanglement entropy for all ball-shaped regions can always be represented geometrically (via the Ryu-Takayanagi formula) by an asymptotically AdS geometry. We show that such a geometry necessarily satisfies Einstein's equations perturbatively up to second order, with a stress energy tensor arising from matter fields associated with the sourced primary operators. We make no assumptions about AdS/CFT duality, so our work serves as both a consistency check for the AdS/CFT correspondence and a direct demonstration that spacetime and gravitational physics can emerge from the description of entanglement in conformal field theories.
hep-th, gr-qc
Faulkner, Thomas
3650f55f-31c0-4e5a-ad86-2abd6576fbb4
Haehl, Felix M.
eb0d74fd-0d8b-4b1b-8686-79d43c2a3a5f
Hijano, Eliot
e6db07ec-1a99-473e-a579-424d3168deb2
Parrikar, Onkar
073eb582-35a8-4336-a731-748fc17cbc11
Rabideau, Charles
f2947b61-a9df-498d-b94c-39798a85e325
Raamsdonk, Mark Van
4df7da2d-5cbd-4e6b-ad7f-83dd0ab63b01
19 August 2017
Faulkner, Thomas
3650f55f-31c0-4e5a-ad86-2abd6576fbb4
Haehl, Felix M.
eb0d74fd-0d8b-4b1b-8686-79d43c2a3a5f
Hijano, Eliot
e6db07ec-1a99-473e-a579-424d3168deb2
Parrikar, Onkar
073eb582-35a8-4336-a731-748fc17cbc11
Rabideau, Charles
f2947b61-a9df-498d-b94c-39798a85e325
Raamsdonk, Mark Van
4df7da2d-5cbd-4e6b-ad7f-83dd0ab63b01
Faulkner, Thomas, Haehl, Felix M., Hijano, Eliot, Parrikar, Onkar, Rabideau, Charles and Raamsdonk, Mark Van
(2017)
Nonlinear gravity from entanglement in conformal field theories.
Journal of High Energy Physics, 2017 (8), [57].
(doi:10.1007/JHEP08(2017)057).
Abstract
In this paper, we demonstrate the emergence of nonlinear gravitational equations directly from the physics of a broad class of conformal field theories. We consider CFT excited states defined by adding sources for scalar primary or stress tensor operators to the Euclidean path integral defining the vacuum state. For these states, we show that up to second order in the sources, the entanglement entropy for all ball-shaped regions can always be represented geometrically (via the Ryu-Takayanagi formula) by an asymptotically AdS geometry. We show that such a geometry necessarily satisfies Einstein's equations perturbatively up to second order, with a stress energy tensor arising from matter fields associated with the sourced primary operators. We make no assumptions about AdS/CFT duality, so our work serves as both a consistency check for the AdS/CFT correspondence and a direct demonstration that spacetime and gravitational physics can emerge from the description of entanglement in conformal field theories.
Text
1705.03026v1
- Accepted Manuscript
More information
Accepted/In Press date: 26 July 2017
Published date: 19 August 2017
Additional Information:
55 pages, 8 figures
Keywords:
hep-th, gr-qc
Identifiers
Local EPrints ID: 470046
URI: http://eprints.soton.ac.uk/id/eprint/470046
ISSN: 1126-6708
PURE UUID: 58686f69-99c0-4404-95f0-f5ec13ee69f7
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Date deposited: 30 Sep 2022 16:52
Last modified: 17 Mar 2024 04:14
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Contributors
Author:
Thomas Faulkner
Author:
Felix M. Haehl
Author:
Eliot Hijano
Author:
Onkar Parrikar
Author:
Charles Rabideau
Author:
Mark Van Raamsdonk
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