Gravitational Dynamics From Entanglement "Thermodynamics"

TL;DR

This paper demonstrates that in holographic conformal field theories, the entanglement entropy relation leads to Einstein's equations governing the dual geometry, linking entanglement thermodynamics to gravitational dynamics.

Contribution

It shows that the entanglement-entropy relation in holographic CFTs implies Einstein's equations at linear order, establishing a connection between entanglement thermodynamics and gravity.

Findings

Entanglement entropy perturbations relate to energy changes in CFTs.

Holographic entanglement entropy corresponds to extremal surface areas.

Linearized Einstein's equations emerge from entanglement relations.

Abstract

In a general conformal field theory, perturbations to the vacuum state obey the relation \delta S = \delta E, where \delta S is the change in entanglement entropy of an arbitrary ball-shaped region, and \delta E is the change in "hyperbolic" energy of this region. In this note, we show that for holographic conformal field theories, this relation, together with the holographic connection between entanglement entropies and areas of extremal surfaces and the standard connection between the field theory stress tensor and the boundary behavior of the metric, implies that geometry dual to the perturbed state satisfies Einstein's equations expanded to linear order about pure AdS.