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Title: A Rényi quantum null energy condition: proof for free field theories

Abstract

The Quantum Null Energy Condition (QNEC) is a lower bound on the stress-energy tensor in quantum field theory that has been proved quite generally. It can equivalently be phrased as a positivity condition on the second null shape derivative of the relative entropy Srel(ρ||σ) of an arbitrary state ρ with respect to the vacuum σ. The relative entropy has a natural one-parameter family generalization, the Sandwiched Rényi divergence Sn(ρ||σ), which also measures the distinguishability of two states for arbitrary n ∈ [1/2, ∞). A Rényi QNEC, a positivity condition on the second null shape derivative of Sn(ρ||σ), was conjectured in previous work. In this work, we study the Rényi QNEC for free and superrenormalizable field theories in spacetime dimension d > 2 using the technique of null quantization. In the above setting, we prove the Rényi QNEC in the case n > 1 for arbitrary states. We also provide counterexamples to the Rényi QNEC for n < 1.

Authors:
ORCiD logo [1];  [2];  [2]
  1. Cornell Univ., Ithaca, NY (United States)
  2. Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Publication Date:
Research Org.:
Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1798154
Grant/Contract Number:  
AC02-05CH11231
Resource Type:
Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2021; Journal Issue: 1; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Citation Formats

Moosa, Mudassir, Rath, Pratik, and Su, Vincent Paul. A Rényi quantum null energy condition: proof for free field theories. United States: N. p., 2021. Web. doi:10.1007/jhep01(2021)064.
Moosa, Mudassir, Rath, Pratik, & Su, Vincent Paul. A Rényi quantum null energy condition: proof for free field theories. United States. https://doi.org/10.1007/jhep01(2021)064
Moosa, Mudassir, Rath, Pratik, and Su, Vincent Paul. Wed . "A Rényi quantum null energy condition: proof for free field theories". United States. https://doi.org/10.1007/jhep01(2021)064. https://www.osti.gov/servlets/purl/1798154.
@article{osti_1798154,
title = {A Rényi quantum null energy condition: proof for free field theories},
author = {Moosa, Mudassir and Rath, Pratik and Su, Vincent Paul},
abstractNote = {The Quantum Null Energy Condition (QNEC) is a lower bound on the stress-energy tensor in quantum field theory that has been proved quite generally. It can equivalently be phrased as a positivity condition on the second null shape derivative of the relative entropy Srel(ρ||σ) of an arbitrary state ρ with respect to the vacuum σ. The relative entropy has a natural one-parameter family generalization, the Sandwiched Rényi divergence Sn(ρ||σ), which also measures the distinguishability of two states for arbitrary n ∈ [1/2, ∞). A Rényi QNEC, a positivity condition on the second null shape derivative of Sn(ρ||σ), was conjectured in previous work. In this work, we study the Rényi QNEC for free and superrenormalizable field theories in spacetime dimension d > 2 using the technique of null quantization. In the above setting, we prove the Rényi QNEC in the case n > 1 for arbitrary states. We also provide counterexamples to the Rényi QNEC for n < 1.},
doi = {10.1007/jhep01(2021)064},
journal = {Journal of High Energy Physics (Online)},
number = 1,
volume = 2021,
place = {United States},
year = {Wed Jan 13 00:00:00 EST 2021},
month = {Wed Jan 13 00:00:00 EST 2021}
}

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