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I Tensor networks, spin networks and loop quantum gravity

  1. Oct 10, 2016 #1
    Loop Quantum Gravity, Exact Holographic Mapping, and Holographic Entanglement Entropy
    Muxin Han, Ling-Yan Hung
    (Submitted on 7 Oct 2016)
    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 Σ with boundary ∂Σ 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 A¯ are specified on the boundary ∂Σ, 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 ∂Σ.
    Comments: 26+1 pages, 5 figures
    Subjects: High Energy Physics - Theory (hep-th); General Relativity and Quantum Cosmology (gr-qc); Quantum Physics (quant-ph)
    Cite as: arXiv:1610.02134 [hep-th]
    (or arXiv:1610.02134v1 [hep-th] for this version)
  2. jcsd
  3. Oct 15, 2016 #2
    Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.
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