Holographic entanglement from the UV to the IR

TL;DR

This paper demonstrates that holographic entanglement entropy remains invariant under bulk RG flow in AdS/CFT, showing agreement between UV and IR calculations and extending the replica method to matter fields with spin.

Contribution

It provides a proof of holographic entanglement entropy invariance under bulk RG flow and generalizes the replica method to include spinning matter fields.

Findings

Holographic entanglement entropy is invariant under bulk RG flow.

Explicit agreement of entropy calculations in UV and IR theories.

Generalization of the replica method to matter fields with spin.

Abstract

In AdS/CFT, observables on the boundary are invariant under renormalization group (RG) flow in the bulk. In this paper, we study holographic entanglement entropy under bulk RG flow and find that it is indeed invariant. We focus on tree-level RG flow, where massive fields in a UV theory are integrated out to give the IR theory. We explicitly show that in several simple examples, holographic entanglement entropy calculated in the UV theory agrees with that calculated in the IR theory. Moreover, we give an argument for this agreement to hold for general tree-level RG flow. Along the way, we generalize the replica method of calculating holographic entanglement entropy to bulk theories that include matter fields with nonzero spin.