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Chinese Physics C

Fixing the AdS3 metric from pure state entanglement entropies of CFT2 *

Peng Wang, Houwen Wu, Haitang Yang

Published Jan 20, 2025• 1 citation
Publisher

Abstract

Abstract In this study, based on the Ryu-Takayanagi formula, by identifying the pure state UV and IR entanglement entropies of a perturbed CFT2 with geodesic lengths in the bulk, we demonstrate that the dual geometry is uniquely determined to be asymptotically AdS3. The pure AdS3 geometry is recovered by taking the massless limit of the system. Our derivations hold in both static and covariant scenarios.

DOI
10.1088/1674-1137/ada960

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A bstract We investigate a new proposal connecting the geometry at various radial scales in asymptotic AdS spacetime with entanglement structure at corresponding real-space length scales of the boundary theory. With this proposal, the bulk IR geometry encodes the long-scale entanglement structure of the dual quantum system. We consider two distinct types of IR geometries, namely the spherical case and the hyperbolic case, which are intimately related to the physics of differential entropy and brane-world holography separately. We explore the corresponding change in the dual long-scale entanglement structures, utilizing the tools of the Ryu-Takayanagi formula, conditional mutual information, and partial entanglement entropy. The results indicate that modifying the IR geometry leads to a redistribution of entanglement at scales longer than a critical length determined by the location of the IR region, with the two modified IR geometries corresponding to two opposite ways of redistribution. Furthermore, we establish the maximum amount of entanglement that can be modified, which is proportional to the area of the IR region.
We substantiate a covariant proposal for the holographic reflected entropy in CFTs dual to non-static AdS geometries from the bulk extremal entanglement wedge cross section in the literature with explicit computations in the AdS3/CFT2 scenario. In this context we obtain the reflected entropy for zero and finite temperature time dependent bipartite mixed states in CFT1+1s with a conserved charge dual to bulk rotating extremal and non-extremal BTZ black holes through a replica technique. Our results match exactly with the corresponding extremal entanglement wedge cross section for these bulk geometries in the literature. This constitutes a significant consistency check for the proposal and its possible extension to the corresponding higher dimensional AdS/CFT scenario.