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تسجيل مستخدم جديدEntanglement between two gravitating universes
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We study two disjoint universes in an entangled pure state. When only one universe contains gravity, the path integral for the $n^{text{th}}$ Renyi 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 $2n$ 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.
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