Gravity Dual of Connes Cocycle Flow
arXiv:2007.00230 · doi:10.1103/PhysRevD.102.066008
Abstract
We define the "kink transform" as a one-sided boost of bulk initial data about the Ryu-Takayanagi surface of a boundary cut. For a flat cut, we conjecture that the resulting Wheeler-DeWitt patch is the bulk dual to the boundary state obtained by Connes cocycle (CC) flow across the cut. The bulk patch is glued to a precursor slice related to the original boundary slice by a one-sided boost. This evades ultraviolet divergences and distinguishes our construction from one-sided modular flow. We verify that the kink transform is consistent with known properties of operator expectation values and subregion entropies under CC flow. CC flow generates a stress tensor shock at the cut, controlled by a shape derivative of the entropy; the kink transform reproduces this shock holographically by creating a bulk Weyl tensor shock. We also go beyond known properties of CC flow by deriving novel shock components from the kink transform.
arXiv comment43 pages, 7 figures
References in corpus (51)
- Gauge Theory Correlators from Non-Critical String Theory
- The Large N Limit of Superconformal Field Theories and Supergravity
- Holographic Derivation of Entanglement Entropy from AdS/CFT
- A Covariant Holographic Entanglement Entropy Proposal
- Eternal Black Holes in AdS
- Quantum Extremal Surfaces: Holographic Entanglement Entropy beyond the Classical Regime
- Quantum corrections to holographic entanglement entropy
- Bulk Locality and Quantum Error Correction in AdS/CFT
- Notes on Some Entanglement Properties of Quantum Field Theory
- Holographic Dual of BCFT
- Reconstruction of Bulk Operators within the Entanglement Wedge in Gauge-Gravity Duality
- Relative entropy equals bulk relative entropy
- Gravitation from Entanglement in Holographic CFTs
- The Gravity Dual of a Density Matrix
- The Ryu-Takayanagi Formula from Quantum Error Correction
- Local subsystems in gauge theory and gravity
- Holographic Entanglement of Purification
- A proof of the generalized second law for rapidly changing fields and arbitrary horizon slices
- 3+1 Formalism and Bases of Numerical Relativity
- Geometry of Generic Isolated Horizons
- Modular Hamiltonians for Deformed Half-Spaces and the Averaged Null Energy Condition
- Bulk locality from modular flow
- Proof of the Quantum Null Energy Condition
- Causal Holographic Information
- Flat entanglement spectra in fixed-area states of quantum gravity
- Modular Hamiltonians on the null plane and the Markov property of the vacuum state
- The Off-Shell Black Hole
- Holographic Renyi Entropy from Quantum Error Correction
- Entanglement Wedge Reconstruction via Universal Recovery Channels
- A General Proof of the Quantum Null Energy Condition
- Decoding the Apparent Horizon: A Coarse-Grained Holographic Entropy
- Entropy on a null surface for interacting quantum field theories and the Bousso bound
- Holographic Proof of the Quantum Null Energy Condition
- Asymptotic symmetries on Killing horizons
- Pulling Out the Island with Modular Flow
- Learning the Alpha-bits of Black Holes
- Light-sheets and AdS/CFT
- A modular toolkit for bulk reconstruction
- Null Geodesics, Local CFT Operators and AdS/CFT for Subregions
- Pure states in the SYK model and nearly- gravity
- A holographic proof of the averaged null energy condition
- Entanglement Wedge Reconstruction using the Petz Map
- Gravitational Positive Energy Theorems from Information Inequalities
- Microcanonical Path Integrals and the Holography of small Black Hole Interiors
- Holographic Order from Modular Chaos
- Constraining Quantum Fields using Modular Theory
- Energy is Entanglement
- One-loop universality of holographic codes
- Ignorance is Cheap: From Black Hole Entropy To Energy-Minimizing States In QFT
- A Lower Bound on the Energy Density in Classical and Quantum Field Theories
- Gravitational Corner Conditions in Holography
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