The Euclidean path integral on elliptic de Sitter defines a no-boundary density matrix whose entropies reduce to vertex operator correlators on non-orientable surfaces, with a one-dimensional global Hilbert space but nontrivial observer Fock spaces.
Boundary States as Holographic Duals of Trivial Spacetimes
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abstract
We study real-space quantum entanglement included in conformally invariant boundary states in conformal field theories (CFTs). First, we argue that boundary states essentially have no real-space entanglement by computing the entanglement entropy when we bipartite the system into two spatial regions. From the viewpoint of holography, this shows that boundary states are dual to trivial spacetimes of zero spactime volume. Next, we point out that a continuous multiscale entanglement renormalization ansatz (cMERA) for any CFTs can be formulated by employing a boundary state as its infrared unentangled state with an appropriate regularization. Exploiting this idea, we propose an approximation scheme of cMERA construction for general CFTs.
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Introduces crosscap quenches in CFTs and holographic models to derive universal entanglement entropy evolution, validated by numerics in spin systems.
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No boundary density matrix in elliptic de Sitter dS/$\mathbb{Z}_2$
The Euclidean path integral on elliptic de Sitter defines a no-boundary density matrix whose entropies reduce to vertex operator correlators on non-orientable surfaces, with a one-dimensional global Hilbert space but nontrivial observer Fock spaces.
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Crosscap Quenches and Entanglement Evolution
Introduces crosscap quenches in CFTs and holographic models to derive universal entanglement entropy evolution, validated by numerics in spin systems.