Inconsistency of Islands in Theories with Long-Range Gravity

TL;DR

This paper investigates the inconsistency of islands in theories with long-range gravity, revealing potential conflicts with gravitational Gauss law and suggesting islands may not form valid entanglement wedges in such theories.

Contribution

It demonstrates that islands in long-range gravity theories conflict with the Gauss law, challenging their validity as entanglement wedges and proposing conditions for their consistency.

Findings

Energy of island excitations can be detected outside the island

Islands are associated with massive gravitons in known examples

Potential inconsistency of islands in massless gravity theories

Abstract

In ordinary gravitational theories, any local bulk operator in an entanglement wedge is accompanied by a long-range gravitational dressing that extends to the asymptotic part of the wedge. Islands are the only known examples of entanglement wedges that are disconnected from the asymptotic region of spacetime. In this paper, we show that the lack of an asymptotic region in islands creates a potential puzzle that involves the gravitational Gauss law, independently of whether or not there is a non-gravitational bath. In a theory with long-range gravity, the energy of an excitation localized to the island can be detected from outside the island, in contradiction with the principle that operators in an entanglement wedge should commute with operators from its complement. In several known examples, we show that this tension is resolved because islands appear in conjunction with a massive graviton. We also derive some additional consistency conditions that must be obeyed by islands in decoupled systems. Our arguments suggest that islands might not constitute consistent entanglement wedges in standard theories of massless gravity where the Gauss law applies.