The Page Curve for Reflected Entropy

• URL: http://arxiv.org/abs/2201.11730v3
• Date: Mon, 17 Jul 2023 16:35:33 GMT
• Title: The Page Curve for Reflected Entropy
• Authors: Chris Akers, Thomas Faulkner, Simon Lin and Pratik Rath
• Abstract summary: We study the reflected entropy $S_R$ in the West Coast Model, a toy model of black hole evaporation consisting of JT gravity coupled to end-of-the-world branes. We analyze the important non-perturbative effects that smooth out the discontinuity in the $S_R$ phase transition. We find that area fluctuations of $O(sqrtG_N)$ spread out the $S_R$ phase transition in the canonical ensemble.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study the reflected entropy $S_R$ in the West Coast Model, a toy model of black hole evaporation consisting of JT gravity coupled to end-of-the-world branes. We demonstrate the validity of the holographic duality relating it to the entanglement wedge cross section away from phase transitions. Further, we analyze the important non-perturbative effects that smooth out the discontinuity in the $S_R$ phase transition. By performing the gravitational path integral, we obtain the reflected entanglement spectrum analytically. The spectrum takes a simple form consisting of superselection sectors, which we interpret as a direct sum of geometries, a disconnected one and a connected one involving a closed universe. We find that area fluctuations of $O(\sqrt{G_N})$ spread out the $S_R$ phase transition in the canonical ensemble, analogous to the entanglement entropy phase transition. We also consider a Renyi generalization of the reflected entropy and show that the location of the phase transition varies as a function of the Renyi parameter.

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