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 $\partial\Sigma$.
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机译：从体边界对偶性和全息纠缠熵的角度探讨了环量子引力（LQG）与张量网络之间的关系。我们发现，空间$ \ Sigma $中具有边界$ \ partial \ Sigma $的LQG自旋网络状态是精确的全息映射，类似于arXiv：1309.6282中的建议。张量网络，被理解为边界量子态，是自旋网络的粗粒度过程中出现的精确全息图的输出。此外，当在边界$ \ partial \ Sigma $上指定了区域$ A $及其补语$ \ bar {A} $时，我们表明紧急张量网络的边界纠缠熵$ S（A）$满足Ryu在这些经典的制度中，高柳公式即$ S（A）$与$ \ partial \ Sigma $中附着于$ A $边界的散装表面的最小面积成比例。
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