Universality of Gravity from Entanglement
By Brian Swingle, Mark Van Raamsdonk. 2014
187 citations recorded by the source corpus.
The entanglement "first law" in conformal field theories relates the entanglement entropy for a ball-shaped region to an integral over the same region involving the expectation value of the CFT stress-energy tensor, for infinitesimal perturbations to the CFT vacuum state. In recent work, this was exploited at leading order in $N$ in the context of large N holographic CFTs to show that any geometry dual to a perturbed CFT state must satisfy Einstein's equations linearized about pure AdS. In this note, we investigate the implications of the leading 1/N correction to the exact CFT result. We show that these corrections give rise to the source term for the gravitational equations: for semiclassical bulk states, the expectation value of the bulk stress-energy tensor appears as a source in the linearized equations. In particular, the CFT first law leads to Newton's Law of gravitation and the fact that all sources of stress-energy source the gravitational field. In our derivation, this universality of gravity comes directly from the universality of entanglement (the fact that all degrees of freedom in a subsystem contribute to entanglement entropy).
Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/72b43c417b8dc473d60a594dd065c9f8287ee68d
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Citations in the corpus
- Emergent Gravity and the Dark Universe (2016, methodology): “For this purpose we will make use of Wald’s formalism [50] and methods similar to those developed in [15, 16, 17] for the derivation of the (linearized) Einstein equations from the area law entanglement.”
- Space from Hilbert Space: Recovering Geometry from Bulk Entanglement (2016, background): “In doing so we will follow some of the logic in [5] and [23].”
- Quantum extremal surfaces: holographic entanglement entropy beyond the classical regime (2014, methodology): “The first quantum corrections to this formula were computed, at order O(N) (boundary) or O(~) (bulk), by Faulkner, Lewkowycz, and Maldacena (FLM); see also [40, 41].”
- Relative entropy equals bulk relative entropy (2015, background): “This is basically the inverse of the argument in [28].”
- Integral geometry and holography (2015, background): “As a result, central tenets of gravitational physics – Einstein’s equations [7– 9], energy conditions [10, 11], even connectedness of spacetime [12–17] – have been reduced to statements about entanglement in the boundary theory.”