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Conformal Description of Near-Horizon Vacuum States
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abstract
Motivated by recent work suggesting observably large spacetime fluctuations in the causal development of an empty region of flat space, we conjecture that these metric fluctuations can be quantitatively described in terms of a conformal field theory of near-horizon vacuum states. One consequence of this conjecture is that fluctuations in the modular Hamiltonian $\Delta K$ of a causal diamond are equal to the entanglement entropy: $\langle \Delta K^2 \rangle = \langle K \rangle = \frac{A(\Sigma_{d-2})}{4 G_d}$, where $A(\Sigma_{d-2})$ is the area of the entangling surface in $d$ dimensions. Our conjecture applies to flat space, the cosmological horizon of dS, and AdS Ryu-Takayanagi diamonds, but not to large finite area diamonds in the bulk of AdS. We focus on three pieces of quantitative evidence, from a Randall-Sundrum II braneworld, from the conformal description of black hole horizons, and from the fluid-gravity correspondence. Our hypothesis also suggests that a broader range of formal results can be brought to bear on observables in flat and dS spaces.
Forward citations
Cited by 7 Pith papers
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Diamonds in the Bulk and Large-$N$ Scaling in AdS/CFT
Bulk field algebras of causal diamonds in AdS/CFT require a double-scaling limit, so sub-AdS-radius distances are not described by bulk QFT.
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From Asymptotically Flat Gravity to Finite Causal Diamonds
The soft sector phase space of asymptotically flat gravity equals the phase space of radial size fluctuations of a finite causal diamond in flat spacetime.
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Entanglement Entropy of Quantum Corners
For a two-dimensional corner symmetry algebra, coherent corner states give an entanglement entropy that scales with the area when mapped to near-extremal Reissner-Nordström black holes.
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Singularities, Entropy and the Arrow of Time, {\it or} Is CRT a Gauge Symmetry in Quantum Gravity?
CRT is an asymptotic gauge symmetry in flat/AdS quantum gravity, not a true gauge symmetry, and is absent or only spontaneously broken under special untestable conditions in de Sitter cosmologies.
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Effective density matrix for vacua in asymptotically flat gravity
The vacuum of a large causal diamond in asymptotically flat gravity is claimed to be a Gaussian in the supertranslation Goldstone mode, giving modular Hamiltonian variance A/epsilon squared.
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JT gravity and deformed CFTs
Deformed CFTs on a strip with a stretched-horizon conformal boundary are proposed as UV completions of pure and matter-coupled JT gravity, reproducing its entropy and a Page-curve-like saturation.
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Correlation functions of von Neumann entropy
Two-point correlators of modular Hamiltonians obey entropy-like properties and equal the stress-tensor conformal block for spherical regions in CFT, including imaginary-time separations.
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