Entanglement between two gravitating universes

We study two disjoint universes in an entangled pure state. When only one universe contains gravity, the path integral for the nth 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 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.

Automated summary

We study the entangled pure state of two disjoint universes. The presence of gravity in one or both universes leads to modifications in the calculation of the entropy. When only one universe has gravity, a wormhole between the copies of the gravitating universe is included in the entropy formula. When both universes have gravity, a novel wormhole with multiple boundaries connecting replica copies of both universes dominates the path integral. The contribution from this wormhole restores unitarity.