Recovering the QNEC from the ANEC

By Fikret Ceyhan, T. Faulkner. Communications in Mathematical Physics, 2018

135 citations recorded by the source corpus.

We study the relative entropy in QFT comparing the vacuum state to a special family of purifications determined by an input state and constructed using relative modular flow. We use this to prove a conjecture by Wall that relates the shape derivative of relative entropy to a variational expression over the averaged null energy (ANE) of possible purifications. This variational expression can be used to easily prove the quantum null energy condition (QNEC). We formulate Wall’s conjecture as a theorem pertaining to operator algebras satisfying the properties of a half-sided modular inclusion, with the additional assumption that the input state has finite averaged null energy. We also give a new derivation of the strong superadditivity property of relative entropy in this context. We speculate about possible connections to the recent methods used to strengthen monotonicity of relative entropy with recovery maps.

Subfields: Geometry and Topology, Mathematical Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/cb68e2dd08e76d4783914a9b68e693e64fc8b1ea

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In Geometry and Topology

1. Eleni-Alexandra Kontou
2. Ahmed Almheiri
3. Ko Sanders
4. J. Maldacena
5. Ashoke Sen

In Mathematical Physics

1. Eleni-Alexandra Kontou
2. Ko Sanders
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In Nuclear and High Energy Physics

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4. J. Maldacena
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Citations in the corpus

• Energy conditions in general relativity and quantum field theory (2020, background): “the fact that the von Neumann entropy is ill-defined, it has nevertheless been argued that under suitable circumstances the QNEC implies the ANEC [139] and, conversely, that the ANEC implies this QNEC [23]. Using somewhat similar arguments, Faulkner et al. have argued that the ANEC can be derived dir”
• Islands outside the horizon (2019, background): “So one might have expected that (12) would follow from the conformal transformation properties of the flat space QNEC that was conjectured in [18] and proven in [19, 20, 21] − 2π T flat ++ + ∂(2) +S ≤ 0 (flat space, proven) .”