# Nonlinear gravity from entanglement in conformal field theories

@article{Faulkner2017NonlinearGF, title={Nonlinear gravity from entanglement in conformal field theories}, author={Thomas Faulkner and Felix M. Haehl and Eliot Hijano and Onkar Parrikar and Charles Rabideau and Mark Van Raamsdonk}, journal={Journal of High Energy Physics}, year={2017}, volume={2017}, pages={1-48} }

A bstractIn this paper, we demonstrate the emergence of nonlinear gravitational equations directly from the physics of a broad class of conformal field theories. We consider CFT excited states defined by adding sources for scalar primary or stress tensor operators to the Euclidean path integral defining the vacuum state. For these states, we show that up to second order in the sources, the entanglement entropy for all ball-shaped regions can always be represented geometrically (via the Ryu…

## 143 Citations

### Higher Curvature Gravity from Entanglement in Conformal Field Theories.

- PhysicsPhysical review letters
- 2018

If an asymptotically anti-de Sitter (AdS) spacetime computes the entanglement entropies of ball-shaped regions in a conformal field theory using a generalized Ryu-Takayanagi formula up to second order in state deformations around the vacuum, then the spacetime satisfies the correct gravitational equations of motion up tosecond order around the AdS background.

### Gravity from entanglement and RG flow in a top-down approach

- Physics
- 2017

A bstractThe duality between a d-dimensional conformal field theory with relevant deformation and a gravity theory on an asymptotically AdSd+1 geometry, has become a suitable tool in the…

### Gravity from entanglement and RG flow in a top-down approach

- PhysicsJournal of High Energy Physics
- 2018

The duality between a d-dimensional conformal field theory with relevant deformation and a gravity theory on an asymptotically AdSd+1 geometry, has become a suitable tool in the investigation of the…

### Brane dynamics from the first law of entanglement

- PhysicsJournal of High Energy Physics
- 2020

In this note, we study the first law of entanglement in a boundary conformal field theory (BCFT) dual to warped AdS cut off by a brane. Exploiting the symmetry of boundary-centered half-balls in the…

### Brane dynamics from the first law of entanglement

- PhysicsJournal of High Energy Physics
- 2020

In this note, we study the first law of entanglement in a boundary conformal field theory (BCFT) dual to warped AdS cut off by a brane. Exploiting the symmetry of boundary-centered half-balls in the…

### Bulk entanglement gravity without a boundary: Towards finding Einstein's equation in Hilbert space

- Physics
- 2018

We consider the emergence from quantum entanglement of spacetime geometry in a bulk region. For certain classes of quantum states in an appropriately factorized Hilbert space, a spatial geometry can…

### The holographic shape of entanglement and Einstein’s equations

- PhysicsJournal of High Energy Physics
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We study shape-deformations of the entanglement entropy and the modular Hamiltonian for an arbitrary subregion and state (with a smooth dual geometry) in a holographic conformal field theory. More…

### Entanglement transfer from quantum matter to classical geometry in an emergent holographic dual description of a scalar field theory

- PhysicsJournal of High Energy Physics
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Applying recursive renormalization group transformations to a scalar field theory, we obtain an effective quantum gravity theory with an emergent extra dimension, described by a dual holographic…

### Effects of non-conformal boundary on entanglement entropy

- PhysicsJournal of High Energy Physics
- 2020

Spacetime boundaries with canonical Neuman or Dirichlet conditions preserve conformal invarience, but “mixed” boundary conditions which interpolate linearly between them can break conformal symmetry…

### The holographic shape of entanglement and Einstein’s equations

- Physics
- 2018

A bstractWe study shape-deformations of the entanglement entropy and the modular Hamiltonian for an arbitrary subregion and state (with a smooth dual geometry) in a holographic conformal field…

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