SciPost Submission Page
Semi-local Bounds on Null Energy in QFT
by Jackson R. Fliss, Ben Freivogel
This Submission thread is now published as
|Authors (as registered SciPost users):||Jackson Fliss|
|Preprint Link:||scipost_202109_00032v2 (pdf)|
|Date submitted:||2021-12-06 22:30|
|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.
Published as SciPost Phys. 12, 084 (2022)
Author comments upon resubmission
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.