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Semi-local Bounds on Null Energy in QFT
by Jackson R. Fliss, Ben Freivogel
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|Authors (as registered SciPost users):||Jackson Fliss|
|Preprint Link:||scipost_202109_00032v1 (pdf)|
|Date submitted:||2021-09-28 12:32|
|Submitted by:||Fliss, Jackson|
|Submitted to:||SciPost Physics|
We investigate whether the null energy, averaged over some region of space- time, is bounded below in QFT. First, we use light-sheet quantization to prove a version of the “Smeared Null Energy Condition” (SNEC) proposed in , applicable for free and super-renormalizable QFT’s equipped with a UV cut- off. Through an explicit construction of squeezed states, we show that the SNEC bound cannot be improved by smearing on a light-sheet alone. We propose that smearing the null energy over two null directions defines an op- erator that is bounded below and independent of the UV cutoff, in what we call the “Double-Smeared Null Energy Condition,” or DSNEC. We indicate schematically how this bound behaves with respect to the smearing lengths and argue that the DSNEC displays a transition when the smearing lengths are comparable to the correlation length.
Reports on this Submission
Report 1 by Aron Wall on 2021-11-8 (Invited Report)
- Cite as: Aron Wall, Report on arXiv:scipost_202109_00032v1, delivered 2021-11-08, doi: 10.21468/SciPost.Report.3817
1. Clearly written and accessible
2. Derives some new results about smeared energy conditions
1. Article does not make very clear what the utility of the new bounds, are compared to past work.
2. Terminology not clearly compatible with past work on SNEC.
This paper has an interesting discussion of smearing the stress tensor in null directions. As far as I can tell the results are valid, though not extremely suprising given past work on smearing the stress-tensor in  and . The authors give a very clear explanation of their work, and citations seem to be adequate.
While this is a good paper which should be published, I'm having difficulty seeing the case for publishing in SciPost Physics given the PRL-like acceptance criteria. I don't feel that any of the 4 Expectations (at least one required) were met. The authors do not spend much time discussing the physical significance or applicability of the bound to physical problems. Since one of the bounds depends on the UV cutoff, and the other seems like a repackaging of a timelike smearing bound, it is not clear that this paper opens up a major new line of investigation.
I think this article should instead be published in SciPost Physics Core.
1. The authors' version of SNEC is not really the same thing as the SNEC defined in , since one bound uses G while the other is a flat space bound defined with a UV cutoff. Authors should consider whether making some sort of explicit terminology distinction between these bounds would be less confusing.