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

Understand

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.