Universality of Gravity from Entanglement

Abstract

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).

arXiv comment23 pages, 2 figures

References in corpus (13)

• Holographic Derivation of Entanglement Entropy from AdS/CFT
• Black Hole Entropy is Noether Charge
• Some Properties of Noether Charge and a Proposal for Dynamical Black Hole Entropy
• Towards a derivation of holographic entanglement entropy
• Generalized gravitational entropy
• Building up spacetime with quantum entanglement
• Holographic Entanglement Entropy: An Overview
• Self-Interaction and Gauge Invariance
• Gravitational Dynamics From Entanglement "Thermodynamics"
• Thermodynamical Property of Entanglement Entropy for Excited States
• Entanglement Temperature and Entanglement Entropy of Excited States
• A hole-ographic spacetime
• Comments on quantum gravity and entanglement

Cited by in corpus (85)

• Quantum Extremal Surfaces: Holographic Entanglement Entropy beyond the Classical Regime
• Emergent Gravity and the Dark Universe
• Relative entropy equals bulk relative entropy
• Holographic Entanglement Entropy
• Entanglement Equilibrium and the Einstein Equation
• Entanglement entropy of electromagnetic edge modes
• Space from Hilbert Space: Recovering Geometry from Bulk Entanglement
• Local phase space and edge modes for diffeomorphism-invariant theories
• Comments on the Necessity and Implications of State-Dependence in the Black Hole Interior
• Subsystem Complexity and Holography
• Bulk Emergence and the RG Flow of Entanglement Entropy
• Canonical Energy is Quantum Fisher Information
• Quantum Information in Holographic Duality
• Nuts and Bolts for Creating Space
• Hawking from Catalan
• Quantum minimal surfaces from quantum error correction
• Renormalization group constructions of topological quantum liquids and beyond
• Towards Bulk Metric Reconstruction from Extremal Area Variations
• Sewing spacetime with Lorentzian threads: complexity and the emergence of time in quantum gravity
• What is the Entropy in Entropic Gravity?
• Entwinement in discretely gauged theories
• Energy is Entanglement
• Comments on Jacobson's "Entanglement equilibrium and the Einstein equation"
• Holographic coherent states from random tensor networks
• Cosmic Equilibration: A Holographic No-Hair Theorem from the Generalized Second Law
• Modular Hamiltonian of a chiral fermion on the torus
• General Results for Higher Spin Wilson Lines and Entanglement in Vasiliev Theory
• RG flow of entanglement entropy to thermal entropy
• The Gravity Dual of Boundary Causality
• A Bound on Holographic Entanglement Entropy from Inverse Mean Curvature Flow
• Entanglement on linked boundaries in Chern-Simons theory with generic gauge groups
• Entanglement entropy of excited states in conformal perturbation theory and the Einstein equation
• Space-time random tensor networks and holographic duality
• Thermodynamic law from the entanglement entropy bound
• On Holographic Entanglement Entropy with Second Order Excitations
• Group Field Theory and Holographic Tensor Networks: Dynamical Corrections to the Ryu-Takayanagi formula
• Complete Einstein equation from the generalized First Law of Entanglement
• BPS Soliton Solutions of a D3-brane Action
• Renormalization Group Circuits for Gapless States
• Explicit reconstruction of the entanglement wedge
• Building Bulk Geometry from the Tensor Radon Transform
• Gravity and On-Shell Probe Actions
• More of the Bulk from Extremal Area Variations
• Double-Trace Deformations and Entanglement Entropy in AdS
• Quantum bit threads and holographic entanglement
• Gravity from entanglement for boundary subregions
• Integral Geometry and Holography
• Bulk area law for boundary entanglement in spin network states: entropy corrections and horizon-like regions from volume correlations
• Comments on universal properties of entanglement entropy and bulk reconstruction
• Bulk Locality and Entanglement Swapping in AdS/CFT
• Nonlocal multi-trace sources and bulk entanglement in holographic conformal field theories
• Large-$d$ phase transitions in holographic mutual information
• Thermofield dynamics and Gravity
• Emergent Gravity in a Holographic Universe
• The thermodynamics of quantum spacetime histories
• Holographic Approach to Entanglement Entropy in Disordered Systems
• Inviolable energy conditions from entanglement inequalities
• Quantum randomness is chimeric
• Entanglement Entropy in Jammed CFTs
• Spacetime-Free Approach to Quantum Theory and Effective Spacetime Structure
• Covariant Momentum Map Thermodynamics for Parametrized Field Theories
• Bulk private curves require large conditional mutual information
• Holographic relations in loop quantum gravity
• 't Hooft suppression and holographic entropy
• Deriving the First Law of Black Hole Thermodynamics without Entanglement
• Gravity from Entanglement and RG Flow in a Top-down Approach
• A Toy Model of Entwinement
• Electric fields and quantum wormholes
• Circuit Complexity in $U(1)$ Gauge Theory
• Perturbative Complexity of Interacting Theory
• A perturbative study on the analytic continuation for generalized gravitational entropy
• First Law of Entanglement Entropy vs Black Hole Entropy in an Anomalous Theory
• Circuit Complexity From Supersymmetric Quantum Field Theory With Morse Function
• Entanglement for Quantum Hall states and a Generalized Chern-Simons Form
• Entanglement entropy and kinematic space in BCFT and RG flow
• The Complexity of Identifying Ryu-Takayanagi Surfaces in AdS3/CFT2
• A Review of the Holographic Relation between Linearized Gravity and the First Law of Entanglement Entropy
• Entanglement Entropy for Open Bosonic Strings on $Dp$-branes
• Emergent Dark Gravity from (Non)Holographic Screens
• Operator Approach to Complexity : Excited States
• Thesis: Tensor networks for dynamic spacetimes
• Strong subadditivity and holography
• Thermal Corrections to Entanglement Entropy from Holography
• Emergence of cosmological Friedmann equations from quantum entanglement
• The generalized first law for more general matter