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arXiv:2211.13246 · Journal of High Energy Physics

Reflected entropy for communicating black holes. Part I. Karch-Randall braneworlds

Mir Afrasiar, Jaydeep Kumar Basak, Ashish Chandra, Gautam Sengupta

Published Feb 20, 2023• 15 citations
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Abstract

A bstract We obtain the reflected entropy for bipartite mixed state configurations of two adjacent and disjoint intervals at a finite temperature in BCFT 2 s with two distinct boundaries through a replica technique in the large central charge limit. Subsequently these field theory results are reproduced from bulk computations involving the entanglement wedge cross section in the dual BTZ black hole geometry truncated by two Karch-Randall branes. Our result confirms the holographic duality between the reflected entropy and the bulk entanglement wedge cross section in the context of the AdS 3 / BCFT 2 scenario. We further investigate the critical issue of the holographic Markov gap between the reflected entropy and the mutual information for these configurations from the bulk braneworld geometry and study its variation with subsystem sizes and time.

DOI
10.1007/jhep02(2023)203

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A bstract We investigate the reflected entropy for various mixed state configurations in the two dimensional holographic conformal field theories sharing a common interface (ICFTs). In the AdS 3 /ICFT 2 framework, we compute the holographic reflected entropy for the required configurations in the vacuum state of the ICFT 2 which is given by twice the entanglement wedge cross section (EWCS) in a spacetime involving two AdS 3 geometries glued along a thin interface brane. Subsequently, we evaluate the EWCS in the bulk geometry involving eternal BTZ black strings with an AdS 2 interface brane, which is dual to an ICFT 2 in the thermofield double (TFD) state. We explore the system from a doubly holographic perspective and determine the island contributions to the reflected entropy in the two dimensional semi-classical description involving two CFT 2 s coupled to an AdS 2 brane. We demonstrate that the results from the island formula match precisely with the bulk AdS 3 results in the large tension limit of the interface brane. We illustrate that the phase structure of the reflected entropy is quite rich involving many novel induced island phases and demonstrate that it obeys the expected Page curve for the reflected entropy in a radiation bath coupled to the AdS 2 black hole.
A bstract We investigate the mixed state entanglement structure through the reflected entropy for disjoint radiation subsystems coupled to a 2d eternal brane world black hole in a time dependent defect AdS 3 /BCFT 2 scenario. Utilizing the island prescription and the defect extremal surface (DES) formula, we demonstrate a complex mixed state entanglement structure through the reflected entropy corresponding to distinct entanglement entropy phases. In each case we verify the holographic duality of the reflected entropy with the bulk entanglement wedge cross section (EWCS) and also obtain the Page curves for both the entanglement entropy and the associated reflected entropy phases. Furthermore, we extend our analysis to adjacent radiation subsystems and obtain consistent results using both the island and the DES prescription.
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Abstract We obtain the odd entanglement entropy (OEE) for bipartite mixed states in ( 1 + 1 ) -dimensional boundary conformal field theories (BCFT 2 s) utilizing an appropriate replica technique. For the generic configuration of two disjoint intervals, the large- c factorization of the twist field correlator leads to several distinct phases depending on the relative sizes and separations of the intervals. The resulting expressions match consistently with the entanglement wedge cross section (EWCS) for the bulk AdS 3 braneworld geometries, thereby extending the proposed holographic duality between the difference of the OEE and the entanglement entropy with the EWCS to BCFT setups. Furthermore, we obtain the OEE for these mixed states in related holographic moving mirror models which simulate Hawking radiation from black holes and verify the above duality in these time-dependent backgrounds. In this context we analyze the time evolution of the OEE and establish the analogues of Page curves for this mixed-state correlation measure.