2014/05/12 by Brian Swingle, Swingle, Brian, Mark Van Raamsdonk +1 · 134 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Noncommutative and Quantum Gravity Theories #Physics #Quantum #Quantum entanglement #Quantum mechanics #Statistical physics #Theoretical physics #Universality (dynamical systems) #gr-qc #hep-th
paper · pdf · doi:10.48550/arxiv.1405.2933
published in arXiv (Cornell University) (Cornell University) · 23 pages, 2 figures
arxiv created 2014/05/12 · openalex publication_date 2014/05/12 · arxiv updated 2014/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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).