Bulk entanglement and its shape dependence

TL;DR

This paper investigates the universal aspects of bulk entanglement entropy in even dimensions, especially four dimensions, revealing shape dependence and a local/nonlocal duality in holographic CFTs, with limitations in higher dimensions.

Contribution

It provides explicit calculations of bulk entanglement entropy for various shapes in four dimensions and uncovers a shape dependence and duality in holographic CFTs.

Findings

Bulk entanglement entropy encodes universal boundary information.

Shape dependence of entanglement entropy matches leading boundary entropy under deformations.

The duality between bulk and boundary entanglement holds in 4D but not in higher dimensions.

Abstract

We study one-loop bulk entanglement entropy in even spacetime dimensions using the heat kernel method, which captures the universal piece of entanglement entropy, a logarithmically divergent term in even dimensions. In four dimensions, we perform explicit calculations for various shapes of boundary subregions. In particular, for a cusp subregion with an arbitrary opening angle, we find that the bulk entanglement entropy always encodes the same universal information about the boundary theories as the leading entanglement entropy in the large N limit, up to a fixed proportional constant. By smoothly deforming a circle in the boundary, we find that to leading order of the deformations, the bulk entanglement entropy shares the same shape dependence as the leading entanglement entropy and hence the same physical information can be extracted from both cases. This establishes an interesting local/nonlocal duality for holographic $\mm{CFT}_3$. However, the result does not hold for higher dimensional holographic theories.