Loop Quantum Gravity, Exact Holographic Mapping, and Holographic Entanglement Entropy

Abstract

The relation between Loop Quantum Gravity (LQG) and tensor network is explored from the perspectives of bulk-boundary duality and holographic entanglement entropy. We find that the LQG spin-network states in a space $\Sigma$ with boundary $\partial \Sigma$ is an exact holographic mapping similar to the proposal in arXiv:1309.6282. The tensor network, understood as the boundary quantum state, is the output of the exact holographic mapping emerging from a coarse graining procedure of spin-networks. Furthermore, when a region $A$ and its complement $\bar{A}$ are specified on the boundary $\partial \Sigma$, we show that the boundary entanglement entropy $S(A)$ of the emergent tensor network satisfies the Ryu-Takayanagi formula in the semiclassical regime, i.e. $S(A)$ is proportional to the minimal area of the bulk surface attached to the boundary of $A$ in $\partial \Sigma$.

26+1 pages, 6 figures, reference added

References in corpus (20)

• Towards a derivation of holographic entanglement entropy
• A class of quantum many-body states that can be efficiently simulated
• Holographic c-theorems in arbitrary dimensions
• Polyhedra in loop quantum gravity
• The Entanglement Renyi Entropies of Disjoint Intervals in AdS/CFT
• Advances on Tensor Network Theory: Symmetries, Fermions, Entanglement, and Holography
• The length operator in Loop Quantum Gravity
• Entanglement Entropy in Loop Quantum Gravity
• Holonomy Spin Foam Models: Definition and Coarse Graining
• Discreteness of the volume of space from Bohr-Sommerfeld quantization
• New length operator for loop quantum gravity
• Coarse graining flow of spin foam intertwiners
• CFT/Gravity Correspondence on the Isolated Horizon
• Black Hole Entropy, Loop Gravity, and Polymer Physics
• Entanglement entropy production in gravitational collapse: covariant regularization and solvable models
• Statistical and entanglement entropy for black holes in quantum geometry
• Reconstructing Quantum Geometry from Quantum Information: Area Renormalisation, Coarse-Graining and Entanglement on Spin Networks
• Quantum gravity at the corner
• The scaling of black hole entropy in loop quantum gravity
• Holographic relations in loop quantum gravity

Cited by in corpus (6)

• The physical meaning of the holographic principle
• Self-Assembly of Geometric Space from Random Graphs
• Holography without holography: How to turn inter-representational into intra-theoretical relations in AdS/CFT
• The multiple realizability of general relativity in quantum gravity
• A Review of the Holographic Relation between Linearized Gravity and the First Law of Entanglement Entropy
• Humeanism in Light of Quantum Gravity