Abstract
We investigate the appearance of islands when a closed universe with gravity is entangled with a non-gravitating quantum system. We use braneworlds in three-dimensional multiboundary wormhole geometries as a model to explore what happens when the non-gravitating system has several components. The braneworld can be either completely contained in the entanglement wedge of one of the non-gravitating systems or split between them. In the former case, entanglement with the other system leads to a mixed state in the closed universe, unlike in simpler setups with a single quantum system, where the closed universe was necessarily in a pure state. We show that the entropy of this mixed state is bounded by half of the coarse-grained entropy of the effective theory on the braneworld.
Highlights
JHEP07(2021)022 according to this prescription is smaller than the effective entropy
We investigate the appearance of islands when a closed universe with gravity is entangled with a non-gravitating quantum system
The derivation of this formula from the path integral [8, 9] tells us that the effective semi-classical state in the island region is encoded in A; semi-classically it looks like we have a seperate Hilbert space HI of the quantum fields on the island, but this is encoded as a code subspace in the Hilbert space HA of the quantum system A
Summary
The model we consider was proposed in [13]; this was further developed in [15,16,17,18]. An intermediate effective theory, where we integrate over the bulk spacetime to obtain an effective gravity theory on the brane; we have a non-gravitational CFT for x < 0 joined across an interface to the same CFT coupled to the brane gravity theory (2.5) for x > 0 This is a useful model to study the appearance of islands in the gravitational theory, by relating them to the classical RT surfaces in the bulk gravity. The brane worldvolume is a closed universe undergoing a big-bang, big-crunch FRW cosmology This bulk spacetime is described by the two-dimensional CFT in the state |Ψ , but we can consider it from the intermediate perspective, where we integrate over the bulk spacetime to obtain an effective theory where we have a CFT coupled to gravity on the brane, entangled with the CFT on the AdS boundary. There is presumably some code subspace of states in the CFT built on |Ψ which encodes excitations in the semi-classical Hilbert space in the closed universe on the brane
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