A Bound on Holographic Entanglement Entropy from Inverse Mean Curvature Flow
arXiv:1612.04373 · doi:10.1088/1361-6382/aa6ad0
Abstract
Entanglement entropies are notoriously difficult to compute. Large-N strongly-coupled holographic CFTs are an important exception, where the AdS/CFT dictionary gives the entanglement entropy of a CFT region in terms of the area of an extremal bulk surface anchored to the AdS boundary. Using this prescription, we show -- for quite general states of (2+1)-dimensional such CFTs -- that the renormalized entanglement entropy of any region of the CFT is bounded from above by a weighted local energy density. The key ingredient in this construction is the inverse mean curvature (IMC) flow, which we suitably generalize to flows of surfaces anchored to the AdS boundary. Our bound can then be thought of as a "subregion" Penrose inequality in asymptotically locally AdS spacetimes, similar to the Penrose inequalities obtained from IMC flows in asymptotically flat spacetimes. Combining the result with positivity of relative entropy, we argue that our bound is valid perturbatively in 1/N, and conjecture that a restricted version of it holds in any CFT.
33+7 pages, 7 figures. v2: addressed referee comments
References in corpus (21)
- Complexity and Shock Wave Geometries
- Holographic c-theorems in arbitrary dimensions
- Entanglement as a Probe of Confinement
- Seeing a c-theorem with holography
- A holographic proof of the strong subadditivity of entanglement entropy
- Ground state entanglement and geometric entropy in the Kitaev's model
- Complexity of Formation in Holography
- Quantum Complexity and Negative Curvature
- A c-theorem for the entanglement entropy
- Universality of Gravity from Entanglement
- Numerical study of entanglement entropy in SU(2) lattice gauge theory
- Entanglement entropy across a deformed sphere
- Tomography from Entanglement
- Some results on the shape dependence of entanglement and Rényi entropies
- Renormalized entanglement entropy
- Entanglement Entropy as a Portal to the Physics of Quantum Spin Liquids
- Lectures on quantum energy inequalities
- c-theorem of the entanglement entropy
- State-Dependent Divergences in the Entanglement Entropy
- Bounds on the local energy density of holographic CFTs from bulk geometry
- Renormalized area and properly embedded minimal surfaces in hyperbolic 3-manifolds
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- Towards Bulk Metric Reconstruction from Extremal Area Variations
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- On Universality of Holographic Results for (2+1)-Dimensional CFTs on Curved Spacetimes
- Shape dependence of renormalized holographic entanglement entropy
- Renormalized entanglement entropy and curvature invariants
- On shape dependence of holographic entanglement entropy in AdS4/CFT3 with Lifshitz scaling and hyperscaling violation
- Energy functionals from Conformal Gravity
- Non-conformal entanglement entropy
- Generalised proofs of the first law of entanglement entropy