One-loop universality of holographic codes

Abstract

Recent work showed holographic error correcting codes to have simple universal features at $O(1/G)$. In particular, states of fixed Ryu-Takayanagi (RT) area in such codes are associated with flat entanglement spectra indicating maximal entanglement between appropriate subspaces. We extend such results to one-loop order ($O(1)$ corrections) by controlling both higher-derivative corrections to the bulk effective action and dynamical quantum fluctuations below the cutoff. This result clarifies the relation between the bulk path integral and the quantum code, and implies that i) simple tensor network models of holography continue to match the behavior of holographic CFTs beyond leading order in $G$, ii) the relation between bulk and boundary modular Hamiltonians derived by Jafferis, Lewkowycz, Maldacena, and Suh holds as an operator equation on the code subspace and not just in code-subspace expectation values, and iii) the code subspace is invariant under an appropriate notion of modular flow. A final corollary requires interesting cancelations to occur in the bulk renormalization-group flow of holographic quantum codes. Intermediate technical results include showing the Lewkowycz-Maldacena computation of RT entropy to take the form of a Hamilton-Jacobi variation of the action with respect to boundary conditions, corresponding results for higher-derivative actions, and generalizations to allow RT surfaces with finite conical angles.

arXiv comment45 pages, 1 figure

References in corpus (36)

• Holographic Derivation of Entanglement Entropy from AdS/CFT
• Aspects of Holographic Entanglement Entropy
• A Covariant Holographic Entanglement Entropy Proposal
• Black Holes: Complementarity or Firewalls?
• Generalized gravitational entropy
• Quantum corrections to holographic entanglement entropy
• Holographic quantum error-correcting codes: Toy models for the bulk/boundary correspondence
• Bulk Locality and Quantum Error Correction in AdS/CFT
• Reconstruction of Bulk Operators within the Entanglement Wedge in Gauge-Gravity Duality
• Relative entropy equals bulk relative entropy
• Holographic duality from random tensor networks
• Maximin Surfaces, and the Strong Subadditivity of the Covariant Holographic Entanglement Entropy
• The Gravity Dual of a Density Matrix
• Causality & holographic entanglement entropy
• An Apologia for Firewalls
• The Ryu-Takayanagi Formula from Quantum Error Correction
• Thermodynamics of Asymptotically Locally AdS Spacetimes
• The Gravity Dual of Renyi Entropy
• Holographic Entanglement Entropy for General Higher Derivative Gravity
• An Infalling Observer in AdS/CFT
• Gauge/Gravity Duality and the Black Hole Interior
• Generalized entropy and higher derivative Gravity
• Bulk locality from modular flow
• Entanglement entropy and nonabelian gauge symmetry
• Flat entanglement spectra in fixed-area states of quantum gravity
• Black Hole Entanglement and Quantum Error Correction
• The Off-Shell Black Hole
• Entropy, Extremality, Euclidean Variations, and the Equations of Motion
• Holographic Renyi Entropy from Quantum Error Correction
• Entanglement Wedge Reconstruction via Universal Recovery Channels
• Holographic Entanglement Entropy for the Most General Higher Derivative Gravity
• Learning the Alpha-bits of Black Holes
• A modular toolkit for bulk reconstruction
• Living on the Edge: A Toy Model for Holographic Reconstruction of Algebras with Centers
• Violations of the Born rule in cool state-dependent horizons
• Modular Flow as a Disentangler

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• Entanglement Wedge Cross Sections Require Tripartite Entanglement
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• Real-time gravitational replicas: Formalism and a variational principle
• Reflected entropy in random tensor networks
• Probing phase transitions of holographic entanglement entropy with fixed area states
• The Page Curve for Reflected Entropy
• Enhanced corrections near holographic entanglement transitions: a chaotic case study
• Relative Entropy of Random States and Black Holes
• Gravity Dual of Connes Cocycle Flow
• Reflected entropy in random tensor networks II: a topological index from the canonical purification
• Stability of the microcanonical ensemble in Euclidean Quantum Gravity
• Entanglement spectrum of geometric states
• A Modified Cosmic Brane Proposal for Holographic Renyi Entropy
• A Tale of Two Butterflies: An Exact Equivalence in Higher-Derivative Gravity
• The Spacetime Geometry of Fixed-Area States in Gravitational Systems
• Rényi entropies and area operator from gravity with Hayward term
• Linearised Second Law for Higher Curvature Gravity and Non-Minimally Coupled Vector Fields
• Path integral and conformal instability in nonlocal quantum gravity
• Entanglement Negativity and Replica Symmetry Breaking in General Holographic States
• Black hole wavefunctions and microcanonical states
• Subsystem entropy in 2d CFT and KdV ETH
• Wormholes with Ends of the World
• Holographic entanglement from the UV to the IR
• Large and Small Corrections to the JLMS Formula from Replica Wormholes
• The area operator and fixed area states in conformal field theories
• A trace inequality for Euclidean gravitational path integrals (and a new positive action conjecture)
• Gravitational thermodynamics without the conformal factor problem: Partition functions and Euclidean saddles from Lorentzian Path Integrals
• Euclidean and complex geometries from real-time computations of gravitational Rényi entropies
• Thermodynamic stability from Lorentzian path integrals and codimension-two singularities
• Perturbative distinguishability of black hole microstates from AdS/CFT correspondence
• Spectral Projections for Density Matrices in Quantum Field Theories