The Page curve for reflected entropy
Abstract
We study the reflected entropy SR 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 SR 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 ($$ \sqrt{G_N} $$ G N ) spread out the SR 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.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Jun 15, 2022
- Source ID
- 10.1007/jhep06(2022)089
Entities
People
- Chris Akers
- Pratik Rath
- Simon Lin
- Thomas Faulkner