Dynamics of Entanglement Entropy from Einstein Equation

TL;DR

This paper explores how entanglement entropy in conformal field theories evolves for weakly excited states, revealing that it obeys differential equations analogous to Einstein's equations via the AdS/CFT correspondence.

Contribution

It establishes a direct link between the dynamics of entanglement entropy and Einstein's equations in the context of AdS/CFT, introducing the concept of entanglement density in higher dimensions.

Findings

Entanglement entropy satisfies differential equations similar to Einstein's equations.

Defined and analyzed the dynamical properties of entanglement density in higher-dimensional CFTs.

Provided a framework connecting gravitational dynamics with quantum entanglement evolution.

Abstract

We study the dynamics of entanglement entropy for weakly excited states in conformal field theories by using the AdS/CFT. This is aimed at a first step to find a counterpart of Einstein equation in the CFT language. In particular, we point out that the entanglement entropy satisfies differential equations which directly correspond to the Einstein equation in several setups of AdS/CFT. We also define a quantity called entanglement density in higher dimensional field theories and study its dynamical property for weakly excited states in conformal field theories.