2016/12/31 by Sebastian Fischetti, Toby Wiseman
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Boundary (topology) #Conjecture #Cosmology and Gravitation Theories #Curvature #Entropy (arrow of time) #Geometry #Inverse #Mathematical analysis #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Pure mathematics #Quantum #Quantum entanglement #Quantum mechanics #Theoretical physics #Upper and lower bounds #gr-qc #hep-th
paper · pdf · doi:10.1088/1361-6382/aa6ad0
published as Class.Quant.Grav. 34 (2017) no.12, 125005 · 33+7 pages, 7 figures. v2: addressed referee comments
openalex publication_date 2017/04/03 · arxiv created 2017/05/29 · arxiv updated 2017/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
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.