Inside Out: Meet The Operators Inside The Horizon

Abstract

Based on the work of Heemskerk, Marolf, Polchinski and Sully (HMPS), we study the reconstruction of operators behind causal horizons in time dependent geometries obtained by acting with shockwaves on pure states or thermal states. These geometries admit a natural basis of gauge invariant operators, namely those geodesically dressed to the boundary along geodesics which emanate from the bifurcate horizon at constant Rindler time. We outline a procedure for obtaining operators behind the causal horizon but inside the entanglement wedge by exploiting the equality between bulk and boundary time evolution, as well as the freedom to consider the operators evolved by distinct Hamiltonians. This requires we carefully keep track of how the operators are gravitationally dressed and that we address issues regarding background dependence. We compare this procedure to reconstruction using modular flow, and illustrate some formal points in simple cases such as AdS${}_2$ and AdS${}_3$.

48 pages, 14 figures

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• Pulling Out the Island with Modular Flow
• Complexity Equals Anything II
• Clocks and Rods in Jackiw-Teitelboim Quantum Gravity
• Towards Black Hole Evaporation in Jackiw-Teitelboim Gravity
• Gauge-invariant observables, gravitational dressings, and holography in AdS
• Rotating traversable wormholes in AdS
• Unruh detectors and quantum chaos in JT gravity
• A Survey of Black Hole Thermodynamics
• The AdS${}_3$ Propagator and the Fate of Locality
• Holographic Coarse-Graining: Correlators from the Entanglement Wedge and Other Reduced Geometries
• Seeing the Entanglement Wedge
• Operator Size for Holographic Field Theories
• Brane dynamics from the first law of entanglement
• Microstate Distinguishability, Quantum Complexity, and the Eigenstate Thermalization Hypothesis
• Relational bulk reconstruction from modular flow