Regular Article - Theoretical Physics
Bulk entanglement and its shape dependence
Department of Astrophysics, School of Physics and Materials Science, Guangzhou University, 510006, Guangzhou, China
Accepted: 12 June 2021
Published online: 5 July 2021
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 . However, the result does not hold for higher dimensional holographic theories.
© The Author(s) 2021
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