Holographic maps from quantum gravity states as tensor networks
arXiv:2105.06454 · doi:10.1103/PhysRevD.105.066005
Abstract
We define bulk/boundary maps corresponding to quantum gravity states in the tensorial group field theory formalism, for quantum geometric models sharing the same type of quantum states of loop quantum gravity. The maps are defined in terms of a partition of the quantum geometric data associated to an open graph into bulk and boundary ones, in the spin representation. We determine the general condition on the entanglement structure of the state that makes the bulk/boundary map isometric (a necessary condition for holographic behaviour), and we analyse different types of quantum states, identifying those that define isometric bulk/boundary maps.
arXiv comment27 pages, 6 figures
References in corpus (53)
- The Large N Limit of Superconformal Field Theories and Supergravity
- Holographic Derivation of Entanglement Entropy from AdS/CFT
- The World as a Hologram
- Area laws for the entanglement entropy - a review
- A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
- Aspects of Holographic Entanglement Entropy
- The holographic principle
- Entanglement renormalization
- 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
- Dimensional Reduction in Quantum Gravity
- Holographic duality from random tensor networks
- Hand-waving and Interpretive Dance: An Introductory Course on Tensor Networks
- Critical behavior of colored tensor models in the large N limit
- Colored Tensor Models - a Review
- A Short Review of Loop Quantum Gravity
- Tensor network states and algorithms in the presence of a global U(1) symmetry
- Tensor network decompositions in the presence of a global symmetry
- Absolute Maximal Entanglement and Quantum Secret Sharing
- Lecture Notes of Tensor Network Contractions
- Tensor Networks for Lattice Gauge Theories with continuous groups
- Tensor network states and algorithms in the presence of a global SU(2) symmetry
- Quantum tetrahedra and simplicial spin networks
- Entanglement renormalization and gauge symmetry
- Bidirectional holographic codes and sub-AdS locality
- Beyond Toy Models: Distilling Tensor Networks in Full AdS/CFT
- Consistency Conditions for an AdS/MERA Correspondence
- Conceptual Aspects of Gauge/Gravity Duality
- Flowing in Group Field Theory Space: a Review
- Holomorphic Factorization for a Quantum Tetrahedron
- From Path Integrals to Tensor Networks for AdS/CFT
- Entanglement entropy of squeezed vacua on a lattice
- The Church of the Symmetric Subspace
- Horizon entropy from quantum gravity condensates
- Exploring the Tensor Networks/AdS Correspondence
- Quasi-local holographic dualities in non-perturbative 3d quantum gravity I - Convergence of multiple approaches and examples of Ponzano-Regge statistical duals
- Random Tensors and Quantum Gravity
- Black Holes as Quantum Gravity Condensates
- Quasi-local holographic dualities in non-perturbative 3d quantum gravity
- Einstein Equation from Covariant Loop Quantum Gravity in Semiclassical Continuum Limit
- Holographic coherent states from random tensor networks
- Group Field theory and Tensor Networks: towards a Ryu-Takayanagi formula in full quantum gravity
- Statistical equilibrium of tetrahedra from maximum entropy principle
- Holographic Tensor Networks in Full AdS/CFT
- Quantum gravity states, entanglement graphs and second-quantized tensor networks
- Fisher Metric, Geometric Entanglement and Spin Networks
- Reconstructing Quantum Geometry from Quantum Information: Area Renormalisation, Coarse-Graining and Entanglement on Spin Networks
- Typicality in spin network states of quantum geometry
- On the fate of the Hoop Conjecture in quantum gravity
- Is Holography Implicit in Canonical Gravity?
- Loop Quantum Gravity's Boundary Maps
- Entanglement entropy and correlations in loop quantum gravity
Cited by in corpus (10)
- Stabilizer entropy of quantum tetrahedra
- Bulk area law for boundary entanglement in spin network states: entropy corrections and horizon-like regions from volume correlations
- Holographic entanglement in spin network states: a focused review
- Intertwiner Entanglement Excitation and Holonomy Operator
- Spherically-symmetric geometries in a matter reference frame as quantum gravity condensates
- Curvature from multipartite entanglement in quantum gravity states
- Einstein's equations and the pseudo-entropy of pseudo-Riemannian information manifolds
- No invariant perfect qubit codes
- Transition Amplitudes in 3D Quantum Gravity: Boundaries and Holography in the Coloured Boulatov Model
- Vertex Representation of Hyperbolic Tensor Networks