Entanglement between two gravitating universes

Journal Article · 13 August 2022 · Classical and Quantum Gravity

DOI: https://doi.org/10.1088/1361-6382/ac3c8b · OSTI ID:1887328

Balasubramanian, Vijay; Kar, Arjun ; Ugajin, Tomonori

Abstract We study two disjoint universes in an entangled pure state. When only one universe contains gravity, the path integral for the n th Rényi entropy includes a wormhole between the n copies of the gravitating universe, leading to a standard ‘island formula’ for entanglement entropy consistent with unitarity of quantum information. When both universes contain gravity, gravitational corrections to this configuration lead to a violation of unitarity. However, the path integral is now dominated by a novel wormhole with 2 n boundaries connecting replica copies of both universes. The analytic continuation of this contribution involves a quotient by ${\mathbb{Z}}_n$ replica symmetry, giving a cylinder connecting the two universes. When entanglement is large, this configuration has an effective description as a ‘swap wormhole’, a geometry in which the boundaries of the two universes are glued together by a ‘swaperator’. This description allows precise computation of a generalized entropy-like formula for entanglement entropy. The quantum extremal surface computing the entropy lives on the Lorentzian continuation of the cylinder/swap wormhole, which has a connected Cauchy slice stretching between the universes—a realization of the ER = EPR idea. The new wormhole restores unitarity of quantum information.

• Research Organization: University of Pennsylvania, Philadelphia, PA (United States)
• Sponsoring Organization: Simons Foundation; USDOE; USDOE Office of Science (SC)
• Grant/Contract Number: SC0013528; SC0020360
• OSTI ID: 1887328
• Journal Information: Classical and Quantum Gravity, Journal Name: Classical and Quantum Gravity Journal Issue: 17 Vol. 39; ISSN 0264-9381
• Publisher: IOP PublishingCopyright Statement
• Country of Publication: United Kingdom
• Language: English