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arXiv · 2606.21081

The Entanglement Wedge Polygon

Kosei Fujiki·Jonathan Harper·Tadashi Takayanagi·Nicolò Zenoni
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Abstract

In this work we consider a particular codimension-1 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 $A_i$ the EWP is defined as the region external to all the individual homology regions $r_{A_i}$ which consists of the intersection of the entanglement wedge EW($A_i$) with the time slice. In vacuum AdS$_3$ and BTZ spacetime, the quantity is topological as a direct consequence of the Gauss-Bonnet theorem. In higher dimensions we make progress by considering a number of concrete examples including vacuum, black brane, and soliton solutions of AdS$_{d+1}$ 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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Kosei Fujiki, Jonathan Harper, Tadashi Takayanagi, Nicolò Zenoni. 2026-07-21. The Entanglement Wedge Polygon. https://arxiv.org/abs/2606.21081

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