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2013

Gravitational Dynamics From Entanglement "Thermodynamics"

Lashkari, Nima, McDermott, Michael B., Van Raamsdonk, Mark

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In a general conformal field theory, perturbations to the vacuum state obey the relation \delta S = \delta E, where \delta S is the change in entanglement entropy of an arbitrary ball-shaped region, and \delta E is the change in "hyperbolic" energy of this region.

In this note, we show that for holographic conformal field theories, this relation, together with the holographic connection between entanglement entropies and areas of extremal surfaces and the standard connection between the field theory stress tensor and the boundary behavior of the metric, implies that geometry dual to the perturbed state satisfies Einstein's equations expanded to linear order about pure AdS.

Gravitational Dynamics From Entanglement "Thermodynamics" · Around

Built on

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Similar

R. C. Myers, “Stress tensors and Casimir energies in the AdS / CFT correspondence,” Phys. Rev. D 60
1999
Cited alongside, same era.
O. Aharony, S. S. Gubser, J. M. Maldacena, H. Ooguri and Y. Oz, “Large N field theories, string theory and gravity,” Phys. Rept. 323
2000
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S. de Haro, S. N. Solodukhin and K. Skenderis, “Holographic reconstruction of space-time and renormalization in the AdS / CFT correspondence,” Commun. Math. Phys. 217
2001
Cited alongside, same era.
S. Ryu and T. Takayanagi, “Holographic derivation of entanglement entropy from AdS/CFT,” Phys. Rev. Lett. 96
2006
Cited alongside, same era.
M. Nozaki, T. Numasawa, A. Prudenziati and T. Takayanagi, “Dynamics of Entanglement Entropy from Einstein Equation,” arXiv:1304.7100 [hep-th]
Original
Cited in the paper.
D. D. Blanco, H. Casini, L. -Y. Hung and R. C. Myers, “Relative Entropy and Holography,” arXiv:1305.3182 [hep-th]
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Cited in the paper.
D. Allahbakhshi, M. Alishahiha and A. Naseh, “Entanglement Thermodynamics,” arXiv:1305.2728 [hep-th]
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Cited in the paper.
G. Wong, I. Klich, L. A. Pando Zayas and D. Vaman, “Entanglement Temperature and Entanglement Entropy of Excited States,” arXiv:1305.3291 [hep-th]
Original
Cited in the paper.

Then

V. E. Hubeny, M. Rangamani and T. Takayanagi, “A Covariant holographic entanglement entropy proposal,” JHEP 0707
Original
2007
Later among the works it cites.
T. Padmanabhan, “Thermodynamical Aspects of Gravity: New insights,” Rept. Prog. Phys. 73
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2010
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E. P. Verlinde, “On the Origin of Gravity and the Laws of Newton,” JHEP 1104
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2011
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H. Casini, M. Huerta and R. C. Myers, “Towards a derivation of holographic entanglement entropy,” JHEP 1105
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2011
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