Fine structure in holographic entanglement and entanglement contour

Qiang Wen

doi:10.1103/PhysRevD.98.106004

paper

Fine structure in holographic entanglement and entanglement contour

arXiv:1803.05552 · doi:10.1103/PhysRevD.98.106004

Abstract

We explore the fine structure of the holographic entanglement entropy proposal (the Ryu-Takayanagi formula) in AdS $_{3}$ /CFT $_{2}$ . With the guidance from the boundary and bulk modular flows we find a natural slicing of the entanglement wedge with the modular planes, which are co-dimension one bulk surfaces tangent to the modular flow everywhere. This gives an one-to-one correspondence between the points on the boundary interval $A$ and the points on the Ryu-Takayanagi (RT) surface $E_{A}$ . In the same sense an arbitrary subinterval $A_{2}$ of $A$ will correspond to a subinterval $E_{2}$ of $E_{A}$ . This fine correspondence indicates that the length of $E_{2}$ captures the contribution $s_{A} (A_{2})$ from $A_{2}$ to the entanglement entropy $S_{A}$ , hence gives the contour function for entanglement entropy. Furthermore we propose that $s_{A} (A_{2})$ in general can be written as a simple linear combination of entanglement entropies of single intervals inside $A$ . This proposal passes several non-trivial tests.

arXiv commentv3:Version improved, second half of the paper re-written, relate the fine structure to the entanglement contour, references added, title changed, calculation details added. v4:published version 21 pages, 9 figures

Fine structure in holographic entanglement and entanglement contour

Abstract

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