Inconsistency of islands in theories with long-range gravity

Journal Article · 28 January 2022 · Journal of High Energy Physics (Online)

DOI: https://doi.org/10.1007/jhep01(2022)182 · OSTI ID:1922350

Geng, Hao ^[1]; Karch, Andreas ^[2]; Perez-Pardavila, Carlos ^[3]; Raju, Suvrat ^[4]; Randall, Lisa ^[5]; Riojas, Marcos ^[3]; Shashi, Sanjit ^[3]

---

1. Harvard Univ., Cambridge, MA (United States); Univ. of Washington, Seattle, WA (United States); University of Texas at Austin
2. Univ. of Washington, Seattle, WA (United States); Univ. of Texas, Austin, TX (United States)
3. Univ. of Texas, Austin, TX (United States)
4. Tata Inst. of Fundamental Research, Bengaluru (India)
5. Harvard Univ., Cambridge, MA (United States)

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.

• Research Organization: Univ. of Texas, Austin, TX (United States)
• Sponsoring Organization: India Department of Science and Technology; Indian Department of Atomic Energy; Moore Foundation; National Science Foundation (NSF); Simons Foundation; USDOE Office of Science (SC)
• Grant/Contract Number: SC0022021
• OSTI ID: 1922350
• Journal Information: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 1 Vol. 2022; ISSN 1029-8479
• Publisher: Springer NatureCopyright Statement
• Country of Publication: United States
• Language: English