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.
27 pages, 6 figures
References in corpus (9)
- A Short Review of Loop Quantum Gravity
- Tensor network states and algorithms in the presence of a global U(1) symmetry
- Tensor Networks for Lattice Gauge Theories with continuous groups
- Entanglement renormalization and gauge symmetry
- Consistency Conditions for an AdS/MERA Correspondence
- From Path Integrals to Tensor Networks for AdS/CFT
- Holographic Tensor Networks in Full AdS/CFT
- Reconstructing Quantum Geometry from Quantum Information: Area Renormalisation, Coarse-Graining and Entanglement on Spin Networks
- Loop Quantum Gravity's Boundary Maps
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- 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