Recovering the QNEC from the ANEC

Ceyhan, Fikret; Faulkner, Thomas

doi:10.1007/s00220-020-03751-y

Title: Recovering the QNEC from the ANEC

Journal Article · Tue May 05 00:00:00 EDT 2020 · Communications in Mathematical Physics

DOI:https://doi.org/10.1007/s00220-020-03751-y· OSTI ID:1843343

Ceyhan, Fikret ^[1]; Faulkner, Thomas ^[1]

Univ. of Illinois at Urbana-Champaign, IL (United States)

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. Furthermore, 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 con- text. We speculate about possible connections to the recent methods used to strengthen monotonicity of relative entropy with recovery maps.

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Research Organization:: Univ. of Illinois at Urbana-Champaign, IL (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: SC0019517

OSTI ID:: 1843343

Journal Information:: Communications in Mathematical Physics, Vol. 377, Issue 2; ISSN 0010-3616

Publisher:: SpringerCopyright Statement

Country of Publication:: United States

Language:: English

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