The entanglement wedge of unknown couplings

The black hole interior is a mysterious region of spacetime where non-perturbative effects are sometimes important. These non-perturbative effects are believed to be highly theory-dependent. We sharpen these statements by considering a setup where the state of the black hole is in a superposition of states corresponding to boundary theories with different couplings, entangled with a reference which keeps track of those couplings. The entanglement wedge of the reference can then be interpreted as the bulk region most sensitive to the values of the couplings. In simple bulk models, e.g., JT gravity + a matter BCFT, the QES formula implies that the reference contains the black hole interior at late times. We also analyze the Renyi-2 entropy tr rho(2) of the reference, which can be viewed as a diagnostic of chaos via the Loschmidt echo. We find explicitly the replica wormhole that diagnoses the island and restores unitarity. Numerical and analytical evidence of these statements in the SYK model is presented. Similar considerations are expected to apply in higher dimensional AdS/CFT, for marginal and even irrelevant couplings. [GRAPHICS] .

Automated summary

The study shows that non-perturbative effects in the interior of black holes depend on the theory, and can be further analyzed by considering the entanglement between the black hole state and a reference state with different couplings. By analyzing the entropy of the reference state and the Loschmidt echo, chaos can be detected and possible islands can be identified to restore unitarity.