Abstract
We study 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 relation for holographic mathrm {CFT}_3. However, the result does not hold for higher dimensional holographic theories.
Highlights
Where Igrav and Imatt denotes the Euclidean action of gravity sector and matter sector, respectively
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 constant proportional to the central charges of the boundary
By studying a smoothly deformed circle in the boundary, we find that the bulk entanglement entropy, which is non-geometric, shares the same shape dependence with the leading, geometric RT formula
Summary
Extending (5) to include the contribution of quantum fluctuations in a fixed background, the bulk entanglement entropy is given by. Where Ief f [Mn] stands for the one-loop effective action in the replica geometry for various quantum fluctuations. We will adopt heat kernel method to evaluate Ief f as well as the bulk entanglement entropy. We will work in Euclidean signature throughout this paper
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