Pole-skipping data encodes enough information to reconstruct the full metric of 3D rotating black holes and the radial functions of 4D separable rotating black holes, with Einstein equations becoming algebraic constraints on that data.
Integral Geometry and Holography
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abstract
We present a mathematical framework which underlies the connection between information theory and the bulk spacetime in the AdS$_3$/CFT$_2$ correspondence. A key concept is kinematic space: an auxiliary Lorentzian geometry whose metric is defined in terms of conditional mutual informations and which organizes the entanglement pattern of a CFT state. When the field theory has a holographic dual obeying the Ryu-Takayanagi proposal, kinematic space has a direct geometric meaning: it is the space of bulk geodesics studied in integral geometry. Lengths of bulk curves are computed by kinematic volumes, giving a precise entropic interpretation of the length of any bulk curve. We explain how basic geometric concepts -- points, distances and angles -- are reflected in kinematic space, allowing one to reconstruct a large class of spatial bulk geometries from boundary entanglement entropies. In this way, kinematic space translates between information theoretic and geometric descriptions of a CFT state. As an example, we discuss in detail the static slice of AdS$_3$ whose kinematic space is two-dimensional de Sitter space.
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Functional renormalization group applied to the O(N) vector model generates an emergent regular AdS_{d+1} geometry whose near-horizon thermodynamics reproduces the first law and Bekenstein-Hawking area law with temperature matching the boundary field theory.
Holographic tensor networks constructed from PEE-thread tessellations of AdS geometry reproduce the exact Ryu-Takayanagi formula in factorized EPR, perfect-tensor, and random variants.
The authors establish the descendant structure of the holographic SO(2,d) anomaly and construct the associated characteristic class, bulk Chern-Simons-like action, boundary effective action, and anomalous conservation laws in covariant and consistent forms.
citing papers explorer
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Probing bulk geometry via pole skipping: from static to rotating spacetimes
Pole-skipping data encodes enough information to reconstruct the full metric of 3D rotating black holes and the radial functions of 4D separable rotating black holes, with Einstein equations becoming algebraic constraints on that data.
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Emergent AdS Geometry and Black Hole Thermodynamics from Functional Renormalization Group
Functional renormalization group applied to the O(N) vector model generates an emergent regular AdS_{d+1} geometry whose near-horizon thermodynamics reproduces the first law and Bekenstein-Hawking area law with temperature matching the boundary field theory.
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Holographic Tensor Networks as Tessellations of Geometry
Holographic tensor networks constructed from PEE-thread tessellations of AdS geometry reproduce the exact Ryu-Takayanagi formula in factorized EPR, perfect-tensor, and random variants.
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Holographic $SO(2,d)$ anomaly
The authors establish the descendant structure of the holographic SO(2,d) anomaly and construct the associated characteristic class, bulk Chern-Simons-like action, boundary effective action, and anomalous conservation laws in covariant and consistent forms.