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A note on the architecture of spacetime geometry
High Energy Physics - Theory · Submitted 20 Jul 2016
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We show that if one literally starts from the full $\text{SL}(2,\mathbb{C})$ group, this procedure naturally leads to the Bekenstein-Hawking formula of the entanglement entropy for any macroscopic spacetime region.
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The abstract, sentence by sentence
Recently the $\text{SU}(2)$ spin-network states in loop quantum gravity is generalized to those of the corresponding affine Lie algebra. We show that if one literally starts from the full $\text{SL}(2,\mathbb{C})$ group, this procedure naturally leads to the Bekenstein-Hawking formula of the entanglement entropy for any macroscopic spacetime region. This suggests that a smooth spacetime geometry could be recovered in such a way, as conjectured by Bianchi and Myers. Some comparison with Xiao-Gang Wen's string-net picture of gauge theory is made.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Recently the $\text{SU}(2)$ spin-network states in loop quantum gravity is generalized to those of the corresponding affine Lie algebra. | background 0.99 | 0.10 | 0.04 | asserted 1.00 |
| s1 | We show that if one literally starts from the full $\text{SL}(2,\mathbb{C})$ group, this procedure naturally leads to the Bekenstein-Hawking formula of the entanglement entropy for any macroscopic spacetime region. | result 0.97 | 0.91 | 0.79 | asserted 1.00 |
| s2 | This suggests that a smooth spacetime geometry could be recovered in such a way, as conjectured by Bianchi and Myers. | interpretation 1.00 | 0.12 | 0.18 | hedged possibility 0.99 |
| s3 | Some comparison with Xiao-Gang Wen's string-net picture of gauge theory is made. | contribution 0.83 | 0.71 | 0.03 | asserted 0.92 |
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The paper
Original abstract
Recently the $\text{SU}(2)$ spin-network states in loop quantum gravity is generalized to those of the corresponding affine Lie algebra. We show that if one literally starts from the full $\text{SL}(2,\mathbb{C})$ group, this procedure naturally leads to the Bekenstein-Hawking formula of the entanglement entropy for any macroscopic spacetime region. This suggests that a smooth spacetime geometry could be recovered in such a way, as conjectured by Bianchi and Myers. Some comparison with Xiao-Gang Wen's string-net picture of gauge theory is made.
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References
How the literature uses it
4 arXiv papers cite this in 10 sentences
Papers citing it · 7 sentences without a confident label
Contests it 1 paper
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It should be pointed out that no simplicity condition has been imposed in such a derivation (which is of course not a proper choice) [ref] .
Simplicity condition and boundary-bulk duality · Stringy quantum geometry · contest 0.76
Cites it as background 2 papers
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While resubmitting this paper a number of related work has appeared [ref] .
Black Hole Horizon Fluffs: Near Horizon Soft Hairs as Microstates of Three Dimensional Black Holes · Introduction · 0.85
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Finally we mention that there has been earlier works in the literature on the relation between LQG and holography, e.g. [ref] , including a recent work on holographic entanglement entropy by Lee Smolin [ref] .
Loop Quantum Gravity, Exact Holographic Mapping, and Holographic Entanglement Entropy · Holography, Tensor Network, and Loop Quantum Gravity · 1.00
What it cites · 47 sentences without a confident label
Uses the method or tool of 1 paper
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We write out the $𝔰𝔬(2,1)_k⊗𝔰𝔬(2,1)_k$ current algebra explicitly, following the notation in [ref] .
The Statistical Mechanics of the (2+1)-Dimensional Black Hole · “Stringy” spin network and entanglement entropy · 0.92
Compares with 6 papers
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Notice that this double-scaling limit is different from the recent analyzes in [ref] .
Four-dimensional Quantum Gravity with a Cosmological Constant from Three-dimensional Holomorphic Blocks · “Stringy” spin network and entanglement entropy · 0.82
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Notice that this double-scaling limit is different from the recent analyzes in [ref] .
SL(2,C) Chern-Simons Theory, a non-Planar Graph Operator, and 4D Loop Quantum Gravity with a Cosmological Constant: Semiclassical Geometry · “Stringy” spin network and entanglement entropy · 0.82
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Notice that this double-scaling limit is different from the recent analyzes in [ref] .
SL(2,C) Chern-Simons Theory, Flat Connections, and Four-dimensional Quantum Geometry · “Stringy” spin network and entanglement entropy · 0.82
Cites as background 3 papers
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In [ref] the full internal Lorentz group, or its cover group $SL(2,ℂ)$, is first reduced to $SU(2)$ as usual.
CFT/Gravity Correspondence on the Isolated Horizon · “Stringy” spin network and entanglement entropy · 0.84
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The relation between the asymptotic and the near horizon algebra of BTZ black holes has also been discussed recently in [ref] .
Soft Heisenberg hair on black holes in three dimensions · “Stringy” spin network and entanglement entropy · 0.93
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The relation between the asymptotic and the near horizon algebra of BTZ black holes has also been discussed recently in [ref] .
Black Hole Horizon Fluffs: Near Horizon Soft Hairs as Microstates of Three Dimensional Black Holes · “Stringy” spin network and entanglement entropy · 0.93
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