Equivalent Equations of Motion for Gravity and Entropy

TL;DR

This paper establishes a correspondence between the wave equation for entanglement entropy in conformal field theories and the linearized Einstein equations in Anti-de Sitter space, using the formalism of kinematic space.

Contribution

It demonstrates the equivalence between gravitational dynamics and a wave equation on kinematic space, connecting bulk Einstein equations with boundary CFT entanglement entropy.

Findings

Wave equation for entanglement entropy matches linearized Einstein equations

Kinematic space formalism links bulk gravity with boundary CFT

Conformal Casimir equation corresponds to gravitational dynamics

Abstract

We demonstrate an equivalence between the wave equation obeyed by the entanglement entropy of CFT subregions and the linearized bulk Einstein equation in Anti-de Sitter pace. In doing so, we make use of the formalism of kinematic space [arXiv:1505.05515] and fields on this space, introduced in [arXiv:1604.03110]. We show that the gravitational dynamics are equivalent to a gauge invariant wave-equation on kinematic space and that this equation arises in natural correspondence to the conformal Casimir equation in the CFT.