A general proof of integer Rényi QNEC
Abstract
We prove the Rényi quantum null energy condition for every integer Rényi order n≥2. In local Poincaré-invariant quantum field theory, this states that the sandwiched Rényi divergence (SRD) of an excited state relative to the vacuum is convex along a future-directed null deformation. We assume that the deformation is realized by the canonical translations of a half-sided modular inclusion and that the divergence is finite for the initial, undeformed algebra. The proof establishes convexity of the SRD along the induced positive contraction semigroup on Haagerup Ln(M), for every non-zero positive initial element. We also establish a Rényi ant formula at every even integer order and, under an additional regularity assumption, at odd integer orders. The Rényi ant formula identifies the negative first null derivative of SRD with a multiple of the infimum of the canonical null-translation energy over vector purifications of an escort state constructed from the excited state and the vacuum.
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BibTeX
@misc{kibe2026general,
title = {{A general proof of integer Rényi QNEC}},
author = {Tanay Kibe and Pratik Roy},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.15272},
eprint = {2605.15272},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.15272},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A general proof of integer Rényi QNEC
AU - Tanay Kibe
AU - Pratik Roy
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2605.15272
UR - https://arxiv.org/abs/2605.15272
AB - We prove the Rényi quantum null energy condition for every integer Rényi order n≥2. In local Poincaré-invariant quantum field theory, this states that the sandwiched Rényi divergence (SRD) of an excited state relative to the vacuum is convex along a future-directed null deformation. We assume that the deformation is realized by the canonical translations of a half-sided modular inclusion and that the divergence is finite for the initial, undeformed algebra. The proof establishes convexity of the SRD along the induced positive contraction semigroup on Haagerup L^n(M), for every non-zero positive initial element. We also establish a Rényi ant formula at every even integer order and, under an additional regularity assumption, at odd integer orders. The Rényi ant formula identifies the negative first null derivative of SRD with a multiple of the infimum of the canonical null-translation energy over vector purifications of an escort state constructed from the excited state and the vacuum.
ER -