Renormalization Group Is the Principle behind the Holographic Entropy Cone

TL;DR

This paper demonstrates that holographic entropy inequalities reflect the structure of the holographic Renormalization Group, linking bulk geometry depth with entanglement wedge properties.

Contribution

It reveals that all holographic entropy inequalities can be interpreted as statements about the depth of entanglement wedges, thus geometrizing the RG flow.

Findings

Holographic entropy inequalities correspond to entanglement wedges reaching different depths.

Saturation of inequalities indicates equal depth of entanglement wedges.

The inequalities encode and safeguard the holographic Renormalization Group structure.

Abstract

We show that every holographic entropy inequality can be recast in the form: "some entanglement wedges reach deeper in the bulk than some other entanglement wedges." When the inequality is saturated, the two sets of wedges reach equally deep. Because bulk depth geometrizes CFT scales, the inequalities enforce and protect the holographic Renormalization Group.