Pairs of large-N 1D CFTs encode generalized free fields on a timelike geodesic in de Sitter space via large-N factorization, 1D conformal symmetry, and split representations of dS Green functions.
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3D near-de Sitter gravity and the soft mode of DSSYK
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abstract
We present a dual gravity interpretation of the complex reparametrization mode $\psi(u)$ that governs the soft dynamics of double-scaled SYK in the presence of a time-dependent Maldacena-Qi coupling. We find that the dual gravity system takes the form of 2+1-dimensional Einstein-de Sitter gravity with an energy distribution localized on a dS$_2$ slice within dS$_3$. The effective SYK equations of motion take the form of the Israel junction conditions across the dS$_2$ slice. We study the 1D effective action of the SYK soft mode and show that it coincides with the effective action derived from 3D Einstein-de Sitter gravity with conformal boundary conditions on $\mathscr{I}^\pm$. The boundary conditions split $\mathscr{I}^\pm$ into two hyperbolic $k=-1$ slices, and the holographic screen is placed at the intersection. We adapt the Gibbons-Hawking calculation of the Schwarzschild-de Sitter entropy to the case with $k=-1$ boundary conditions and find that it reproduces the semiclassical DSSYK entropy. The boundary-to-boundary Green functions in 3D de Sitter are equal to the square of DSSYK two-point functions. We give an alternative holographic interpretation of our results in terms of 3D AdS gravity with two time directions.
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Proposes an SL(2,Z) sum of Kerr-lens geometries in 3d dS gravity whose spectral density is computed via crosscap amplitudes in CLS ⊗ CLS, matching semi-classical predictions and reducing in a simple case to GΣ ⊗ GΣ on the observer worldline.
Inhomogeneous torus boundaries in 3D gravity are thermodynamically favourable for AdS in the range 2 < K |Λ|^{-1/2} < 3/√2 and support macroscopic entropy for all Λ.
A saddle point in the coupled SYK model yields a bulk geometry with a baby universe whose chord-diagram Hilbert space state is entangled with the exterior, giving evidence that closed universes can carry nontrivial quantum information.
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Generalized Free Fields in de Sitter from 1D CFT
Pairs of large-N 1D CFTs encode generalized free fields on a timelike geodesic in de Sitter space via large-N factorization, 1D conformal symmetry, and split representations of dS Green functions.
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An observer's quantization of 3d de Sitter
Proposes an SL(2,Z) sum of Kerr-lens geometries in 3d dS gravity whose spectral density is computed via crosscap amplitudes in CLS ⊗ CLS, matching semi-classical predictions and reducing in a simple case to GΣ ⊗ GΣ on the observer worldline.
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Undulating Conformal Boundaries in 3D Gravity
Inhomogeneous torus boundaries in 3D gravity are thermodynamically favourable for AdS in the range 2 < K |Λ|^{-1/2} < 3/√2 and support macroscopic entropy for all Λ.
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Baby Universe in a Coupled SYK Model
A saddle point in the coupled SYK model yields a bulk geometry with a baby universe whose chord-diagram Hilbert space state is entangled with the exterior, giving evidence that closed universes can carry nontrivial quantum information.
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