Gravitation from entanglement in holographic CFTs

By T. Faulkner, Monica Guica, Thomas Hartman, R. Myers, Mark Van Raamsdonk. 2013

606 citations recorded by the source corpus.

A bstractEntanglement entropy obeys a ‘first law’, an exact quantum generalization of the ordinary first law of thermodynamics. In any CFT with a semiclassical holographic dual, this first law has an interpretation in the dual gravitational theory as a constraint on the spacetimes dual to CFT states. For small perturbations around the CFT vacuum state, we show that the set of such constraints for all ball-shaped spatial regions in the CFT is exactly equivalent to the requirement that the dual geometry satisfy the gravitational equations of motion, linearized about pure AdS. For theories with entanglement entropy computed by the Ryu-Takayanagi formula S = $ \mathcal{A} $/(4GN), we obtain the linearized Einstein equations. For theories in which the vacuum entanglement entropy for a ball is computed by more general Wald functionals, we obtain the linearized equations for the associated higher-curvature theories. Using the first law, we also derive the holographic dictionary for the stress tensor, given the holographic formula for entanglement entropy. This method provides a simple alternative to holographic renormalization for computing the stress tensor expectation value in arbitrary higher derivative gravitational theories.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/a006789d7334e7d5f840278f738d685028f2562c

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

1. D. Harlow
2. R. Myers
3. S. Raju
4. V. Hubeny
5. J. Maldacena
6. T. Takayanagi
7. D. Stanford
8. Aitor Lewkowycz

In Nuclear and High Energy Physics

1. D. Harlow
2. R. Myers
3. S. Raju
4. J. Maldacena
5. D. Stanford
6. T. Takayanagi
7. V. Hubeny
8. Aitor Lewkowycz

In Statistical and Nonlinear Physics

1. D. Harlow
2. S. Raju
3. R. Myers
4. D. Stanford
5. Aitor Lewkowycz
6. Xi Dong
7. V. Hubeny
8. J. Maldacena

Citations in the corpus

• Universality of Gravity from Entanglement (2014, methodology): “For our generalization to the next order in GN , we will take the same approach as [14], so it will be useful to recall some of the detailed steps in the derivation.”
• Low-dimensional de Sitter quantum gravity (2019, background): “[87–97]), it should be fruitful to import these ideas to study the emergence of time in de Sitter.”
• Remarks on the necessity and implications of state-dependence in the black hole interior (2015, methodology): “2 Equations of motion from the first law of entanglement Another approach of deriving the bulk from the boundary, which has attracted attention, is the program of deriving the bulk equations of motion from the “first law of entanglement” [29, 30, 31].”
• Entropy, extremality, euclidean variations, and the equations of motion (2017, methodology): “This framework naturally allow us to derive the integrated equations of motion by assuming that the entanglement entropy is given by the area thus generalizing [16, 17].”
• The holographic entropy cone (2015, methodology): “A Riemann surface with a constant negative curvature metric can be lifted to a locally AdS3 Lorentzian manifold [26].”
• Shape dependence of entanglement entropy in conformal field theories (2015, neutral): “It has also become clear that entanglement will play a crucial role in understanding the emergence of geometry in the AdS/CFT correspondence [14, 15].”
• Emergent Gravity and the Dark Universe (2016, methodology): “5Here we use the notation of [15] by introducing the symbol εab = 1 (d−2)!εabc1 .”
• Comments on holographic complexity (2016, neutral): “, [54, 55].”
• The AdS/CFT correspondence (2014, methodology): “Under certain special conditions, [167] have been able to use the holographic entanglement entropy proposal to derive linearized Einstein equations in the bulk.”
• Complexity of formation in holography (2016, background): “Again these coordinates only cover a portion of the full AdS geometry, and in particular, the infinite hyperbolic geometry only covers a portion of the boundary time slice at t = 0 and r → ∞ — see figure 2 in [23].”
• A stereoscopic look into the bulk (2016, background): “• a new construction for local bulk operators [12–19]; • a novel look at the modular Hamiltonian [7]; • the origin of geodesic Witten diagrams and their use in computing conformal blocks [20–22]; • and a re-derivation of Einstein’s equations from entanglement (along the lines of [23–25]), whose deta”
• Black hole chemistry: thermodynamics with Lambda (2016, background): “32) has been shown [22] to follow from the bulk gravitational first law associated with the minimal surface Σ.”
• Nonlinear gravity from entanglement in conformal field theories (2017, background): “At the surface Ã, ξA vanishes and we can show that [9, 33] ∫”