Canonical purification and the quantum extremal shock

We study the canonical purification of pure, bi-partite states (with respect to one of the parties) obtained by turning on sources in the Euclidean path integral. In holographic conformal field theories, the Lorentzian bulk dual of the canonical purification consists of the corresponding entanglement wedge glued to its CRT image at the quantum extremal surface. However, the mismatch in the classical expansions at the QES due to quantum corrections needs to be supported by a shock in the bulk matter stress tensor in order for the bulk to satisfy Einstein's equations. Working perturbatively to first order in double-trace sources around the thermofield double state, we demonstrate that the state of the bulk matter in the dual to the canonically purified boundary CFT state precisely has this quantum extremal shock in the bulk stress tensor. We interpret our results as the emergence of gravitational physics from the CFT entanglement structure in a context where bulk quantum corrections are important.

Automated summary

We study the canonical purification of bi-partite states and find that the Lorentzian bulk dual consists of the entanglement wedge and the CRT image, but with a mismatch due to quantum corrections that requires a shock in the bulk matter stress tensor. By perturbatively working with double-trace sources, we demonstrate that the bulk matter state in the dual exactly has this quantum extremal shock in the stress tensor, indicating the emergence of gravitational physics from the CFT entanglement structure in the presence of quantum corrections.