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Peer-reviewedCC BY 4.0Journal of High Energy Physics

The entanglement wedge polygon

  • Kosei Fujiki1
  • Jonathan Harper1,2
  • Tadashi Takayanagi1,3
  • Nicolò Zenoni1
  1. 1Kyoto University
  2. 2Case Western Reserve University
  3. 3Inamori Research Institute for Science
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Abstract

In this work we consider a particular codimension-one region of a holographic spacetime which we call the entanglement wedge polygon (EWP). For a pure state and a partition of the boundary into a number of regions Ai the EWP is defined as the region with maximal volume external to all the individual homology regions rAi which consist of the intersection of the entanglement wedge EW(Ai) with the time slice. In three dimensions, when the EWP has constant curvature as in vacuum AdS3 and BTZ spacetime, its volume is topological as a direct consequence of the Gauss-Bonnet theorem. The topological nature is lost in the time-dependent covariant case and in the presence of an end-of-the-world brane. In higher dimensions we make progress by considering a number of concrete examples including vacuum, black brane, and soliton solutions of AdSd+1 as well as spacetime geometries with end-of-the-world branes dual to boundary conformal field theories. We provide a suitable generalization to mixed states and comment on possible connections between the EWP and measures of multi-partite entanglement.

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Cite

BibTeXRIS
BibTeX
@article{fujiki2026entanglement,
  title = {{The entanglement wedge polygon}},
  author = {Kosei Fujiki and Jonathan Harper and Tadashi Takayanagi and Nicolò Zenoni},
  journal = {Journal of High Energy Physics},
  year = {2026},
  month = nov,
  doi = {10.1007/jhep11(2026)071},
  url = {https://link.springer.com/article/10.1007/JHEP11(2026)071},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - The entanglement wedge polygon
AU  - Kosei Fujiki
AU  - Jonathan Harper
AU  - Tadashi Takayanagi
AU  - Nicolò Zenoni
PY  - 2026
DA  - 2026/11/06
JO  - Journal of High Energy Physics
DO  - 10.1007/jhep11(2026)071
UR  - https://link.springer.com/article/10.1007/JHEP11(2026)071
AB  - In this work we consider a particular codimension-one region of a holographic spacetime which we call the entanglement wedge polygon (EWP). For a pure state and a partition of the boundary into a number of regions Ai the EWP is defined as the region with maximal volume external to all the individual homology regions r_A_i which consist of the intersection of the entanglement wedge EW(Ai) with the time slice. In three dimensions, when the EWP has constant curvature as in vacuum AdS3 and BTZ spacetime, its volume is topological as a direct consequence of the Gauss-Bonnet theorem. The topological nature is lost in the time-dependent covariant case and in the presence of an end-of-the-world brane. In higher dimensions we make progress by considering a number of concrete examples including vacuum, black brane, and soliton solutions of AdSd+1 as well as spacetime geometries with end-of-the-world branes dual to boundary conformal field theories. We provide a suitable generalization to mixed states and comment on possible connections between the EWP and measures of multi-partite entanglement.
SN  - 1029-8479
ER  -