Abstract
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 AdS3/ICFT2 framework, we compute the holographic reflected entropy for the required configurations in the vacuum state of the ICFT2 which is given by twice the entanglement wedge cross section (EWCS) in a spacetime involving two AdS3 geometries glued along a thin interface brane. Subsequently, we evaluate the EWCS in the bulk geometry involving eternal BTZ black strings with an AdS2 interface brane, which is dual to an ICFT2 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 CFT2s coupled to an AdS2 brane. We demonstrate that the results from the island formula match precisely with the bulk AdS3 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 AdS2 black hole.
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Acknowledgments
The research work of JKB supported by the National Science and Technology Council of Taiwan with the grant 112-2636-M-110-006. The work of VM was supported by the NRF grant funded by the Korea government (MSIT) (No. 2022R1A2C1003182) and by the Brain Pool program funded by the Ministry of Science and ICT through the National Research Foundation of Korea (RS-2023-00261799). HP acknowledges the support of this work by the NCTS, Taiwan. The work of GS is partially supported by the Dr Jagmohan Garg Chair Professor position at the Indian Institute of Technology, Kanpur.
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Basak, J.K., Basu, D., Malvimat, V. et al. Holographic reflected entropy and islands in interface CFTs. J. High Energ. Phys. 2024, 143 (2024). https://doi.org/10.1007/JHEP05(2024)143
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DOI: https://doi.org/10.1007/JHEP05(2024)143