Proves integer Rényi QNEC by establishing log-convexity of Kosaki L^n norms under null-translation semigroups for σ-finite von Neumann algebras with half-sided modular inclusions, assuming only finite sandwiched Rényi divergence to the vacuum.
Holographic Proof of the Quantum Null Energy Condition
4 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
We use holography to prove the Quantum Null Energy Condition (QNEC) at leading order in large-$N$ for CFTs and relevant deformations of CFTs in Minkowski space which have Einstein gravity duals. Given any codimension-2 surface $\Sigma$ which is locally stationary under a null deformation in the direction $k$ at the point $p$, the QNEC is a lower bound on the energy-momentum tensor at $p$ in terms of the second variation of the entropy to one side of $\Sigma$: $\langle T_{kk}\rangle \geq S"/2\pi \sqrt{h}$. In a CFT, conformal transformations of this inequality give results which apply when $\Sigma$ is not locally stationary. The QNEC was proven previously for free theories, and taken together with our result this provides strong evidence that the QNEC is a true statement about quantum field theory in general.
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hep-th 4representative citing papers
No Rényi-type divergence obeying DPI, tensor additivity and matched cq conditioning admits a universal off-diagonal quantum focusing inequality.
Derives new state-independent lower bounds on semi-local integrals of null energy flux in QFTs of two and higher dimensions using QNEC, strong subadditivity, and modular Hamiltonians.
Replica analysis shows QNEC saturation in interacting CFTs with twist gap because only the stress-tensor defect operator produces the contact term in the n to 1 limit.
citing papers explorer
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A general proof of integer R\'enyi QNEC
Proves integer Rényi QNEC by establishing log-convexity of Kosaki L^n norms under null-translation semigroups for σ-finite von Neumann algebras with half-sided modular inclusions, assuming only finite sandwiched Rényi divergence to the vacuum.
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No off-diagonal quantum focusing for R\'enyi divergences
No Rényi-type divergence obeying DPI, tensor additivity and matched cq conditioning admits a universal off-diagonal quantum focusing inequality.
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Curious QNEIs from QNEC: New Bounds on Null Energy in Quantum Field Theory
Derives new state-independent lower bounds on semi-local integrals of null energy flux in QFTs of two and higher dimensions using QNEC, strong subadditivity, and modular Hamiltonians.
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Entropy Variations and Light Ray Operators from Replica Defects
Replica analysis shows QNEC saturation in interacting CFTs with twist gap because only the stress-tensor defect operator produces the contact term in the n to 1 limit.