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The relation between Loop Quantum Gravity (LQG) and tensor network isexplored from the perspectives of bulk-boundary duality and holographicentanglement entropy. We find that the LQG spin-network states in a space$\Sigma$ with boundary $\partial\Sigma$ is an exact holographic mapping similarto the proposal in arXiv:1309.6282. The tensor network, understood as theboundary quantum state, is the output of the exact holographic mapping emergingfrom 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 theemergent tensor network satisfies the Ryu-Takayanagi formula in thesemiclassical regime, i.e. $S(A)$ is proportional to the minimal area of thebulk surface attached to the boundary of $A$ in $\partial\Sigma$.

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