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The inheritance of energy conditions: Revisiting no-go theorems in string compactifications
by Heliudson Bernardo, Suddhasattwa Brahma, Mir Mehedi Faruk
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Submission summary
| Authors (as registered SciPost users): | Heliudson Bernardo · Suddhasatwa Brahma |
| Submission information | |
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| Preprint Link: | scipost_202303_00035v1 (pdf) |
| Date submitted: | 2023-03-28 04:32 |
| Submitted by: | Bernardo, Heliudson |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
One of the fundamental challenges in string theory is to derive realistic four-dimensional cosmological backgrounds from it and it has been recently shown that there are strict consistency conditions which must be satisfied in string compactifications, thus constraining its possible low-energy backgrounds. In this work, we focus on energy conditions as \textit{covariant and background independent} consistency requirements in order to classify possible backgrounds coming from low-energy string theory in two steps. Firstly, we show how supergravity actions typically obey many relevant energy conditions, under some reasonable assumptions. Remarkably, we find that the energy conditions are satisfied even in the presence of objects which individually violate them due to the tadpole cancellation condition. Thereafter, we list a set of conditions for a higher-dimensional energy condition to imply the corresponding lower-dimensional one, thereby categorizing the allowed low-energy solutions. As for any no-go theorem, our aim is to highlight the assumptions which must be circumvented for deriving four-dimensional spacetimes that necessarily violate these energy conditions, with emphasis on cosmological backgrounds.
Current status:
Reports on this Submission
Report #2 by Anonymous (Referee 2) on 2023-7-11 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202303_00035v1, delivered 2023-07-11, doi: 10.21468/SciPost.Report.7492
Report
In this paper the authors study the various energy conditions of general relativity (null, strong, weak and dominant) for supergravity fields and D-brane/O-plane sources, finding that they obey these conditions, assuming (in the case of O-planes) that their charges are cancelled by D-branes as required by the tadpole condition.
Furthermore, the authors show a set of sufficient conditions for a higher-dimensional energy condition to imply a lower dimensional one.
The paper contains sufficient important new results, and is clearly written, so I would be happy to recommend publication. I would nevertheless like the authors to consider the following points.
Requested changes
1) The authors show that orientifold planes alone not satisfying the energy conditions, but together with D-branes if the total charge is cancelled as tadpole cancelation condition requires, the system satisfies the conditions. But, as they mention in the conclusions, tadpole cancelation conditions can be satisfied with fluxes and not necessarily D-branes, or in general with D-branes but such that their charge does not totally cancel that of orientifold planes. In the text, as well as in the conclusions (footnote 4) they say that this extra coupling should not affect the results. I do not understand how is that possible, their result assumes a total cancelation of O-plane charge
by D-branes, and since this is no longer true in the presence of fluxes, I cannot see how the latter do not affect their results.
2) Below Eq. (62) the authors say that for an internal manifold with "mean negative Ricci curvature" the WEC is inherited. I imagine by mean negative Ricci curvature they mean the integral over the manifold of the Ricci curvature is negative. But in (62) this is not what they have, there is a factor $\Omega^{d/2}$ that can change the result for a sufficiently strong $\Omega$ in regions where the Ricci curvature is positive. Besides this, I find it counterintuitive that the manifolds that work for the inheritance conditions are the negatively curved ones, as these are typically the ones that could lead most straightforwardly to de Sitter solutions.
Other minor points:
3) In the abstract the authors say "it has been recently shown that there are strict consistency conditions...". I am not sure what reference(s) they are thinking of. In the text they cite the Maldacena-Nuñez no-go, Ref. 5, which is 23 years old and can hardly qualify as "recent". If they are thinking about the whole recent progress that has been done on that front, it might be good to rephrase that.
4) In the introduction "The Gibbons-Maldacena-Nuñez no go...". The sentence does not make too much sense, I do not know what the authors are trying to say.
5) In the discussion the authors say "it must be emphasised that it is more worthwhile to take a more holistic view...". I do not agree it is so obviously more worthwhile, this is the authors' opinion, so I would suggest to clarify that this is a subjective statement.
Typos:
-Below Eq. (10) "the WEC energy conditionS is satisfied"
-First item in the conclusions "are a sufficient conditions"
-Second item: "for we to have"
-Last sentence is not proper English, please rephrase
Report #1 by Anonymous (Referee 3) on 2023-6-19 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202303_00035v1, delivered 2023-06-19, doi: 10.21468/SciPost.Report.7378
Report
In this paper, the authors study various aspects of energy conditions in string compactifications. In particular, they study the null, strong, weak and dominant energy conditions in settings where p-form fields and their sources (D-branes and O-planes) are present.
In particular, the authors observe that although some sources do not individually satisfy them, the cancellation of topological tadpoles required by consistency of the equations of motion entails energy conditions. As a result, consistent configurations of the relevant extended objects in string theory are also fine from this point of view.
The other main section of the paper explores the relation between energy conditions in a higher-dimensional theory and its compactifications, and the main finding is that, at least within rather generic assumptions, the lower-dimensional energy conditions follow from the higher-dimensional ones.
The paper is clearly written and the authors approach an important topic with a holistic view, which can provide a different and useful perspective when exploring the string landscape. The authors also carefully mention various caveats to their analysis, such as higher-curvature and/or string-loop corrections, the presence of scalar potentials in non-supersymmetric settings and the existence of other kinds of more exotic sources, such as S-branes.
All in all, I recommend the paper for publication.
Author: Heliudson Bernardo on 2023-07-24 [id 3832]
(in reply to Report 2 on 2023-07-11)Dear Anonymous Referee,
The authors thank you for reading our work and for the report. We reply to the requested changes as follows:
Our response: We agree that fluxes will change the tadpole cancellation condition used in section 2.3, and recognize that in our conclusion section (see the last paragraph on page 15). However, the analysis in section 2.1 about the validity of the energy conditions by $p$-form fields is not changed because the extra Chen-Simons terms in the $p$-form action will not change their energy-momentum tensor. To highlight that, we wrote footnote 4.
Our response: By mean curvature, we meant precisely the left-hand side of the inequality (62). We admit that this requires extra clarification, so we slightly changed the text below (62). About the referee's intuition, since the WEC is satisfied for dS spacetime, we couldn't find any contradictions in our results.
Other minor points raised by the referee
Our response: We had in mind the more recent progress indeed. We have rephrased the sentence as the referee suggested.
Our response: We meant essentially the SEC inheritance. We have rephrased the sentence for clarification.
Our response: We agree that taking a holistic view of the problem is our opinion. We have rephrased the sentence to make that explicit.
We thank the referee for spotting the typos. We have corrected them accordingly.
We hope this addresses all the referee's concerns and that our work can be published.
Best wishes, Heliudson Bernardo (on behalf of the authors)