The Entanglement Wedge Duality and Hilbert Space Factorization in AdS/CFT, Karch–Randall Braneworld and Black Hole Physics

The entanglement wedge duality in AdS/CFT, Karch–Randall braneworld and black hole (BH) physics is discussed, critically (as in critiques) revolving around Terashima (2024) and Mathur (2009). Emphasis are placed on the semiclassicality requirement and potential breakdown of bulk-wise effective Hilbert space factorization between the BH exterior and the interior, supported by various examples. In particular, a simple quasi-paradox for the entanglement wedge duality in AdS/BCFT is put forward, suggesting that it is not possible to have all of semiclassicality, the entanglement wedge duality and bulk-wise Hilbert space factorization in Karch–Randall braneworld. Giving up factorization, a toy qudit model of BCFT is developed as to derive purification of the BH exterior, despite mostly sharing the setup with the small corrections theorem of Mathur (2009). Put together, the entanglement wedge duality is yet to be disproved despite some results by Terashima, and a toy qudit model cannot disprove semiclassicality in BH physics. The precise understanding of the duality also helps identify how the BH information paradox is dissolved within double holography beyond Karch–Randall braneworld setups.