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Semilocal Bounds on Null Energy in QFT
by Jackson R. Fliss, Ben Freivogel
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Submission summary
Authors (as registered SciPost users):  Jackson Fliss 
Submission information  

Preprint Link:  scipost_202109_00032v1 (pdf) 
Date submitted:  20210928 12:32 
Submitted by:  Fliss, Jackson 
Submitted to:  SciPost Physics 
Ontological classification  

Academic field:  Physics 
Specialties: 

Approach:  Theoretical 
Abstract
We investigate whether the null energy, averaged over some region of space time, is bounded below in QFT. First, we use lightsheet quantization to prove a version of the “Smeared Null Energy Condition” (SNEC) proposed in [1], applicable for free and superrenormalizable 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 lightsheet 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 “DoubleSmeared 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.
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Submission & Refereeing History
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Reports on this Submission
Report 1 by Aron Wall on 2021118 (Invited Report)
 Cite as: Aron Wall, Report on arXiv:scipost_202109_00032v1, delivered 20211108, doi: 10.21468/SciPost.Report.3817
Strengths
1. Clearly written and accessible
2. Derives some new results about smeared energy conditions
Weaknesses
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.
Report
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 stresstensor in [1] and [29]. 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 PRLlike 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.
Requested changes
1. The authors' version of SNEC is not really the same thing as the SNEC defined in [1], 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.
Author: Jackson Fliss on 20211126 [id 1974]
(in reply to Report 1 by Aron Wall on 20211108)We thank Dr. Wall for his insightful comments on our manuscript and for his suggested improvements. After taking into account Dr. Wall’s comments, we would maintain that SciPost Physics is the appropriate section for publishing this manuscript, for the following reasons:
(1) In this manuscript we prove a version of the SNEC directly from field theory and valid in a large class of theories. While acknowledging that this bound makes explicit use of a UV cutoff, it is still a relevant and potentially useful bound for effective field theories (which have a physically motivated cutoff scale and are often relevant deformations of Gaussian theories). Additionally, assuming that a reasonable UV cutoff should be much less than the inverse Planck length, our proof gives strong credence to the original SNEC proposal in a regime where it would not be directly verifiable, say, via holography. Given the SNEC’s established utility in semiclassical gravity (e.g. [Freivogel, Kontou, Krommydas; 2020]) we feel that this result is a significant addition to the literature. With that in mind, we are grateful for Dr. Wall’s suggestion to better distinguish the quantity we prove from the original proposed SNEC, to avoid equivocation. In our revision we will take care in our Introduction to clearly state this distinction and to explain the relation to the SNEC as originally proposed, as well as clarify the points above.
(2) We would like to emphasize that the DSNEC proposed in this paper is logically distinct from timelike worldline inequalities. While one can derive worldline inequalities from the DSNEC (as illustrated in the manuscript), it is not clear that one can derive the DSNEC from foliating a diamond in the $(x^0,x^1)$ plane with worldline inequalities, say, due to the pinching of the worldlines at the corners. We acknowledge a pervading understanding that quantities smeared over timelike domains have finite lower bounds, however we believe that our result manifests this understanding in a way previously unexplored in the literature. An additional novelty to the above is the motivation of the DSNEC as a way to regulating bounds along a null geodesics (such as the field theory SNEC) in a cutoffindependent manner: here the regulator appears directly from thinly smearing in the other null direction as opposed to appearing from a UV sensitive cutoff. Of course, our conjectured bound is more general than the above situation, however this motivation is logically distinct, say, from smearing the null energy along a timelike worldline. We plan to make the novelty of this result mentioned above clearer in our revision.
We hope that Dr. Wall will find our comments and a soontobesubmitted revision satisfactory.
J.R. Fliss, B. Freivogel