The Entanglement Wedge of Unknown Couplings

TL;DR

This paper investigates how the entanglement wedge of a reference system encodes the black hole interior when the boundary theory has unknown or varying couplings, using models like JT gravity and SYK.

Contribution

It introduces a framework where the entanglement wedge of a reference captures the black hole interior in superpositions of theories with different couplings, extending the understanding of non-perturbative effects.

Findings

The reference's entanglement wedge includes the black hole interior at late times.

Replica wormholes diagnose the island and restore unitarity.

Evidence from SYK model supports the theoretical framework.

Abstract

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 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.