A modular toolkit for bulk reconstruction

Abstract

We introduce new tools for studying modular flow in AdS/CFT. These tools allow us to efficiently extract bulk information related to causality and locality. For example, we discuss the relation between analyticity in modular time and entanglement wedge nesting which can then be used to extract the location of the Ryu-Takayanagi (RT) surface directly from the boundary theory. Probing the RT surface close to the boundary our results reduce to the recent proof of the Quantum Null Energy Condition. We focus on heavy probe operators whose correlation functions are determined by spacelike geodesics. These geodesics interplay with the RT surface via a set of rules that we conjecture and give evidence for using the replica trick.

arXiv comment31 pages, 10 figures, v2: typos fixed and references added

References in corpus (42)

• The Large N Limit of Superconformal Field Theories and Supergravity
• Holographic Derivation of Entanglement Entropy from AdS/CFT
• M Theory As A Matrix Model: A Conjecture
• Thermodynamics of Spacetime: The Einstein Equation of State
• A bound on chaos
• A Covariant Holographic Entanglement Entropy Proposal
• Black holes and the butterfly effect
• Generalized gravitational entropy
• Quantum corrections to holographic entanglement entropy
• Entanglement Renormalization and Holography
• Holographic quantum error-correcting codes: Toy models for the bulk/boundary correspondence
• Bulk Locality and Quantum Error Correction in AdS/CFT
• Holography from Conformal Field Theory
• Notes on Some Entanglement Properties of Quantum Field Theory
• Writing CFT correlation functions as AdS scattering amplitudes
• Reconstruction of Bulk Operators within the Entanglement Wedge in Gauge-Gravity Duality
• Relative entropy equals bulk relative entropy
• Entanglement negativity in quantum field theory
• Holographic duality from random tensor networks
• Analyticity in Spin in Conformal Theories
• Maximin Surfaces, and the Strong Subadditivity of the Covariant Holographic Entanglement Entropy
• The Gravity Dual of a Density Matrix
• Causality & holographic entanglement entropy
• A Quantum Focussing Conjecture
• $\mathcal{N}=1$ supersymmetric indices and the four-dimensional A-model
• State-Dependent Bulk-Boundary Maps and Black Hole Complementarity
• Holographic Particle Detection
• Causality Constraints in Conformal Field Theory
• Averaged Null Energy Condition from Causality
• Inside the Horizon with AdS/CFT
• Proof of the Quantum Null Energy Condition
• Bulk locality from modular flow
• On geodesic propagators and black hole holography
• The Entanglement Renyi Entropies of Disjoint Intervals in AdS/CFT
• A Proof of the Conformal Collider Bounds
• Holographic Proof of the Quantum Null Energy Condition
• Fine structure in holographic entanglement and entanglement contour
• Holographic Signatures of Cosmological Singularities
• Towards a Reconstruction of General Bulk Metrics
• Extension of the structure theorem of Borchers and its application to half-sided modular inclusions
• Modular Flow as a Disentangler
• Fermion Families from Two Layer Warped Extra Dimensions

Cited by in corpus (54)

• Beyond Toy Models: Distilling Tensor Networks in Full AdS/CFT
• Shocks, Superconvergence, and a Stringy Equivalence Principle
• Pulling Out the Island with Modular Flow
• Sewing spacetime with Lorentzian threads: complexity and the emergence of time in quantum gravity
• Reflected Entropy and Entanglement Wedge Cross Section with the First Order Correction
• Quantum vs. classical information: operator negativity as a probe of scrambling
• Gravitational Regge bounds
• A Modular Sewing Kit for Entanglement Wedges
• Holographic Order from Modular Chaos
• One-loop universality of holographic codes
• Modular Flow of Excited States
• Bit threads, Einstein's equations and bulk locality
• Relative entropy for coherent states from Araki formula
• Modular Hamiltonians in flat holography and (W)AdS/WCFT
• Gravity Dual of Connes Cocycle Flow
• Comments on black hole interiors and modular inclusions
• Towards classification of holographic multi-partite entanglement measures
• Modular Commutators in Conformal Field Theory
• Barrier from chaos: operator entanglement dynamics of the reduced density matrix
• Modular Hamiltonian for (holographic) excited states
• Emergence of spacetime from the algebra of total modular Hamiltonians
• An intuitive construction of modular flow
• Entanglement Wedge Reconstruction of Infinite-dimensional von Neumann Algebras using Tensor Networks
• Symmetry-resolved modular correlation functions in free fermionic theories
• Bulk reconstruction using timelike entanglement in (A)dS
• Berry phases, wormholes and factorization in AdS/CFT
• Holographic measurement in CFT thermofield doubles
• Local Poincaré Algebra from Quantum Chaos
• Resolving modular flow: a toolkit for free fermions
• Surface growth scheme for bulk reconstruction and tensor network
• Scattering strings off quantum extremal surfaces
• Quantum bit threads and holographic entanglement
• Bridging two quantum quench problems -- local joining quantum quench and Möbius quench -- and their holographic dual descriptions
• The action of HRT-areas as operators in semiclassical gravity
• Quantum Error Correction in SYK and Bulk Emergence
• Entanglement Entropy and Modular Hamiltonian of free fermion with deformations on a torus
• Can one hear the shape of a wormhole?
• Note on surface growth approach for bulk reconstruction
• Explicit reconstruction of the entanglement wedge via the Petz map
• Modular Hamiltonians for Euclidean Path Integral States
• Constraining higher order gravities with subregion duality
• Spectrum of Modular Hamiltonian in the Vacuum and Excited States
• The Algebraic Structure Underlying Pole-Skipping Points
• A Note on Entanglement Entropy for Primary Fermion Fields in JT Gravity
• Boundary and bulk notions of transport in the AdS${}_3$/CFT${}_2$ correspondence
• Virasoro algebras, kinematic space and the spectrum of modular Hamiltonians in CFT${}_2$
• Perturbative expansions of Rényi relative divergences and holography
• Causal shadow and non-local modular flow: from degeneracy to perturbative genesis by correlation
• Position and momentum operators for a moving particle in bulk
• Aspects of Entanglement Entropy in Algebraic Quantum Field Theory
• Modular Intersections, Time Interval Algebras and Emergent AdS${}_2$
• Coarse-Grained Fixed-Point Tensor Networks and Holographic Reflected Entropy in 3D Gravity
• Quantum Information Approaches to Quantum Gravity
• A note on the kinematic space associated with a subregion