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Semi-local 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_00032v2  (pdf)
Date accepted: 2022-02-10
Date submitted: 2021-12-06 22:30
Submitted by: Fliss, Jackson
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • High-Energy Physics - Theory
Approach: Theoretical


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 [1], 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.

Author comments upon resubmission

After taking into account the suggestions and comments from the referee, we are submitting a minor revision that implements the points that we brought up in our response. A detailed list of the changes can be found below.

We hope that this submission better clarifies the novelty and utility of our results as well appropriately distinguishes our SNEC result from its original context, as requested by the referee.

-J.R. Fliss, B. Freivogel

List of changes

1) Added remarks to paragraph below equation (3) in the Introduction to distinguish the SNEC result from the SNEC originally proposed in the context of semi-classical gravity. Added remark in the same paragraph on how this result gives credence to the original SNEC and added a reference.

2) Expanded the first paragraph of the Discussion to remark on the utility of the SNEC result in the context of effective field theories and to elaborate on the relation of the result to the original SNEC.

3) Added paragraph to Discussion (third paragraph) emphasizing the novelty of the proposed DSNEC compared to known worldline inequalities.

Published as SciPost Phys. 12, 084 (2022)

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