The entropic boundary law in BF theory
arXiv:0805.2536 · doi:10.1016/j.nuclphysb.2008.08.004
Abstract
We compute the entropy of a closed bounded region of space for pure 3d Riemannian gravity formulated as a topological BF theory for the gauge group SU(2) and show its holographic behavior. More precisely, we consider a fixed graph embedded in space and study the flat connection spin network state without and with particle-like topological defects. We regularize and compute exactly the entanglement for a bipartite splitting of the graph and show it scales at leading order with the number of vertices on the boundary (or equivalently with the number of loops crossing the boundary). More generally these results apply to BF theory with any compact gauge group in any space-time dimension.
17 pages
References in corpus (17)
- Quantum entanglement
- Fault-tolerant quantum computation by anyons
- Geometric and Renormalized Entropy in Conformal Field Theory
- On Geometric Entropy
- Quantum Information and Relativity Theory
- Bipartite entanglement and entropic boundary law in lattice spin systems
- 3d Quantum Gravity and Effective Non-Commutative Quantum Field Theory
- Lectures on Loop Quantum Gravity
- Ponzano-Regge model revisited I: Gauge fixing, observables and interacting spinning particles
- QSD IV : 2+1 Euclidean Quantum Gravity as a model to test 3+1 Lorentzian Quantum Gravity
- Quantum Black Holes: Entropy and Entanglement on the Horizon
- Spectra of Length and Area in 2+1 Lorentzian Loop Quantum Gravity
- Spin Networks for Non-Compact Groups
- Bulk Entropy in Loop Quantum Gravity
- Reconstructing Quantum Geometry from Quantum Information: Area Renormalisation, Coarse-Graining and Entanglement on Spin Networks
- Entropy, holography and the second law
- Quantum information in loop quantum gravity
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