Entanglement between two gravitating universes

TL;DR

This paper explores entanglement between two universes with gravity, revealing novel wormhole configurations that restore unitarity and connect entanglement with spacetime geometry through the ER=EPR idea.

Contribution

It introduces a new wormhole geometry connecting two gravitating universes and a generalized entropy formula, advancing understanding of entanglement and unitarity in quantum gravity.

Findings

A wormhole with 2n boundaries connects two universes in entangled states.

The swap wormhole provides a geometric interpretation of entanglement.

The new configuration restores unitarity in gravitational entanglement scenarios.

Abstract

We study two disjoint universes in an entangled pure state. When only one universe contains gravity, the path integral for the $n^{\text{th}}$ R\'enyi 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.