Building Tensor Networks for Holographic States

Abstract

We discuss a one-parameter family of states in two-dimensional holographic conformal field theories which are constructed via the Euclidean path integral of an effective theory on a family of hyperbolic slices in the dual bulk geometry. The effective theory in question is the CFT flowed under a $T\overline{T}$ deformation, which "folds" the boundary CFT towards the bulk time-reflection symmetric slice. We propose that these novel Euclidean path integral states in the CFT can be interpreted as continuous tensor network (CTN) states. We argue that these CTN states satisfy a Ryu-Takayanagi-like minimal area upper bound on the entanglement entropies of boundary intervals, with the coefficient being equal to $\frac{1}{4G_N}$; the CTN corresponding to the bulk time-reflection symmetric slice saturates this bound. We also argue that the original state in the CFT can be written as a superposition of such CTN states, with the corresponding wavefunction being the bulk Hartle-Hawking wavefunction.

arXiv comment38 pages, 6 figures

References in corpus (67)

• Holographic Derivation of Entanglement Entropy from AdS/CFT
• A Stress Tensor for Anti-de Sitter Gravity
• A Covariant Holographic Entanglement Entropy Proposal
• Generalized gravitational entropy
• Entanglement renormalization
• Quantum Extremal Surfaces: Holographic Entanglement Entropy beyond the Classical Regime
• 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
• Complexity and Shock Wave Geometries
• Time Evolution of Entanglement Entropy from Black Hole Interiors
• Holography from Conformal Field Theory
• On space of integrable quantum field theories
• $T\bar{T}$-deformed 2D Quantum Field Theories
• Holographic Dual of BCFT
• Reconstruction of Bulk Operators within the Entanglement Wedge in Gauge-Gravity Duality
• Relative entropy equals bulk relative entropy
• Holographic duality from random tensor networks
• Aspects of AdS/BCFT
• The Ryu-Takayanagi Formula from Quantum Error Correction
• Asymptotic Fragility, Near $Ad{S}_2$ Holography and $T\bar{T}$
• Liouville Action as Path-Integral Complexity: From Continuous Tensor Networks to AdS/CFT
• Anti-de Sitter Space from Optimization of Path Integrals in Conformal Field Theories
• Entanglement renormalization for quantum fields
• Cutoff AdS${}_3$ versus the $T\bar{T}$ deformation
• The $T\overline{T}$ deformation of quantum field theory as random geometry
• $T\bar{T}$ Partition Function from Topological Gravity
• Holographic Geometry of Entanglement Renormalization in Quantum Field Theories
• Surface/State Correspondence as a Generalized Holography
• Holography at finite cutoff with a $T^2$ deformation
• cMERA as Surface/State Correspondence in AdS/CFT
• AdS${}_3$ gravity and random CFT
• Bit threads and holographic entanglement
• Bra-ket wormholes in gravitationally prepared states
• Modular invariance and uniqueness of $T\bar{T}$ deformed CFT
• Codimension two holography for wedges
• Entanglement entropy and $T\overline{T}$ deformation
• Flat entanglement spectra in fixed-area states of quantum gravity
• $T\bar{T}$ deformed partition functions
• Holographic Renyi Entropy from Quantum Error Correction
• Tensor Networks from Kinematic Space
• Bidirectional holographic codes and sub-AdS locality
• $T\bar{T}$ and EE, with implications for (A)dS subregion encodings
• Complexity and the bulk volume, a new York time story
• Beyond Toy Models: Distilling Tensor Networks in Full AdS/CFT
• Consistency Conditions for an AdS/MERA Correspondence
• $T\bar{T}$ Deformations, Massive Gravity and Non-Critical Strings
• Hamiltonian deformations in quantum mechanics, $T\bar{T}$, and SYK
• Holographic Spacetimes as Quantum Circuits of Path-Integrations
• Correlation functions, entanglement and chaos in the $T\bar{T}$/$J\bar{T}$-deformed CFTs
• Riemannian and Lorentzian flow-cut theorems
• Sphere partition functions and cut-off AdS
• From Path Integrals to Tensor Networks for AdS/CFT
• Membrane theory of entanglement dynamics from holography
• Holo-ween
• Exploring the Tensor Networks/AdS Correspondence
• Gravity Edges Modes and Hayward Term
• A tensor network quotient takes the vacuum to the thermal state
• Gravitational path integral from the $T^2$ deformation
• Expectation value of $\mathrm{T}\overline{\mathrm{T}}$ operator in curved spacetimes
• Geometrizing $T\bar{T}$
• The Holographic Shape of Entanglement and Einstein's Equations
• Path-Integral Optimization from Hartle-Hawking Wave Function
• $T\bar{T}$ Deformation and the Complexity=Volume Conjecture
• Complexity and Emergence of Warped ${\text{AdS}}_3$ Space-time from Chiral Liouville Action
• Tensor networks for dynamic spacetimes

Cited by in corpus (16)

• A pedagogical review on solvable irrelevant deformations of 2d quantum field theory
• de Sitter Microstates from $T\bar{T}+{\Lambda }_2$ and the Hawking-Page Transition
• Cauchy Slice Holography: A New AdS/CFT Dictionary
• Complexity Growth in Integrable and Chaotic Models
• Quantum complexity in gravity, quantum field theory, and quantum information science
• Islands with Gravitating Baths: Towards ER = EPR
• Holographic Path-Integral Optimization
• Quantum gravity states, entanglement graphs and second-quantized tensor networks
• Path Integral Complexity and Kasner singularities
• Q-curvature and Path Integral Complexity
• Entanglement Renormalization of a $T\bar{T}$-deformed CFT
• $T\bar{T}$ deformed scattering happens within matrices
• On the stabilizer complexity of Hawking radiation
• Cost of holographic path integrals
• York time in JT gravity
• Impact of conversion-driven processes on singlet-doublet Majorana dark matter relic