Gravity from entanglement and RG flow in a top-down approach

O-Kab Kwon (Department of Physics, BK21 Physics Research Division, Institute of Basic Science, Sungkyunkwan University, Suwon, 440-746, South Korea) ; Dongmin Jang (Department of Physics, BK21 Physics Research Division, Institute of Basic Science, Sungkyunkwan University, Suwon, 440-746, South Korea) ; Yoonbai Kim (Department of Physics, BK21 Physics Research Division, Institute of Basic Science, Sungkyunkwan University, Suwon, 440-746, South Korea) ; D.D. Tolla (Department of Physics, BK21 Physics Research Division, Institute of Basic Science, Sungkyunkwan University, Suwon, 440-746, South Korea; University College, Sungkyunkwan University, Suwon, 440-746, South Korea)

The duality between a d-dimensional conformal field theory with relevant deformation and a gravity theory on an asymptotically AdS d+1 geometry, has become a suitable tool in the investigation of the emergence of gravity from quantum entanglement in field theory. Recently, we have tested the duality between the mass-deformed ABJM theory and asymptotically AdS4 gravity theory, which is obtained from the KK reduction of the 11-dimensional supergravity on the LLM geometry. In this paper, we extend the KK reduction procedure beyond the linear order and establish non-trivial KK maps between 4-dimensional fields and 11-dimensional fluctuations. We rely on this gauge/gravity duality to calculate the entanglement entropy by using the Ryu-Takayanagi holographic formula and the path integral method developed by Faulkner. We show that the entanglement entropies obtained using these two methods agree when the asymptotically AdS4 metric satisfies the linearized Einstein equation with nonvanishing energy-momentum tensor for two scalar fields. These scalar fields encode the information of the relevant deformation of the ABJM theory. This confirms that the asymptotic limit of LLM geometry is the emergent gravity of the quantum entanglement in the mass-deformed ABJM theory with a small mass parameter. We also comment on the issue of the relative entropy and the Fisher information in our setup.

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      "surname": "Kim", 
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      "value": "The duality between a d-dimensional conformal field theory with relevant deformation and a gravity theory on an asymptotically AdS d+1 geometry, has become a suitable tool in the investigation of the emergence of gravity from quantum entanglement in field theory. Recently, we have tested the duality between the mass-deformed ABJM theory and asymptotically AdS4 gravity theory, which is obtained from the KK reduction of the 11-dimensional supergravity on the LLM geometry. In this paper, we extend the KK reduction procedure beyond the linear order and establish non-trivial KK maps between 4-dimensional fields and 11-dimensional fluctuations. We rely on this gauge/gravity duality to calculate the entanglement entropy by using the Ryu-Takayanagi holographic formula and the path integral method developed by Faulkner. We show that the entanglement entropies obtained using these two methods agree when the asymptotically AdS4 metric satisfies the linearized Einstein equation with nonvanishing energy-momentum tensor for two scalar fields. These scalar fields encode the information of the relevant deformation of the ABJM theory. This confirms that the asymptotic limit of LLM geometry is the emergent gravity of the quantum entanglement in the mass-deformed ABJM theory with a small mass parameter. We also comment on the issue of the relative entropy and the Fisher information in our setup."
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Published on:
03 May 2018
Publisher:
Springer
Published in:
Journal of High Energy Physics , Volume 2018 (2018)
Issue 5
Pages 1-36
DOI:
https://doi.org/10.1007/JHEP05(2018)009
Copyrights:
The Author(s)
Licence:
CC-BY-3.0

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