Entanglement between two gravitating universes
arXiv:2104.13383 · doi:10.1088/1361-6382/ac3c8b
Abstract
We study two disjoint universes in an entangled pure state. When only one universe contains gravity, the path integral for the Rényi entropy includes a wormhole between the 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 boundaries connecting replica copies of both universes. The analytic continuation of this contribution involves a quotient by 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.
arXiv comment39 pages, 11 figures
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