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Dilaton in scalar QFT: a no-go theorem in 4-epsilon dimensions
by Daniel Nogradi, Balint Ozsvath
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Submission summary
| Authors (as registered SciPost users): | Daniel Nogradi |
| Submission information | |
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| Preprint Link: | scipost_202201_00001v1 (pdf) |
| Date submitted: | 2022-01-04 16:27 |
| Submitted by: | Nogradi, Daniel |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
Spontaneous scale invariance breaking and the associated Goldstone boson, the dilaton, is investigated in renormalizable, unitary, interacting non-supersymmetric scalar field theories in $4-\varepsilon$ dimensions. At leading order it is possible to construct models which give rise to spontaneous scale invariance breaking classically and indeed a massless dilaton can be identified. Beyond leading order, in order to have no anomalous scale symmetry breaking in QFT, the models need to be defined at a Wilson-Fisher fixed point with exact conformal symmetry. It is shown that this requirement on the couplings is incompatible with having the type of flat direction which would be necessary for an exactly massless dilaton. As a result spontaneous scale symmetry breaking and an exactly massless dilaton can not occur in renormalizable, unitary $4-\varepsilon$ dimensional scalar QFT.
Current status:
Reports on this Submission
Report #2 by Anonymous (Referee 3) on 2022-3-25 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202201_00001v1, delivered 2022-03-25, doi: 10.21468/SciPost.Report.4772
Strengths
The arguments given are elementary and are only applied at one loop. I dare say the results about the absence of a dilaton in purely scalar theories in the epsilon expansion are correct but are hardly conclusive about the absence more generally in non supersymmetric theories.
Weaknesses
The main argument in section 4 is almost trivial and rather transcends the examples given in previous sections.
Report
This paper makes a rather minor point but perhaps this has not been made explicitly before and so to this extent the paper has originality.
Requested changes
Are there examples in the literature where dilatons are known in non unitary theories? Are such examples easy to construct? Perhaps a few comments in this direction might be added.
Report #1 by Andreas Stergiou (Referee 1) on 2022-3-11 (Invited Report)
- Cite as: Andreas Stergiou, Report on arXiv:scipost_202201_00001v1, delivered 2022-03-11, doi: 10.21468/SciPost.Report.4605
Strengths
1- Good presentation
2- Pedagogical treatment
3- Solid and simple proof in section 4
Weaknesses
1- Work may not contain enough new results to warrant publication in current state
Report
This manuscript proves that conformal fixed points in scalar models in $d=4-\varepsilon$ have potentials that do not allow for spontaneous scale symmetry breaking (SSSB). The authors begin with a discussion of classical potentials that display SSSB and proceed to show that when quantum mechanical corrections are taken into account, the generated couplings under renormalization are such that SSSB is not possible. The proof provided is simple and mathematically correct.
This manuscript deserves publication as it adds to the knowledge we have about the behavior of conformal field theories in the $\varepsilon$ expansion below $d=4$. However, one could argue that the result presented may not be enough on its own to warrant publication.
My suggestion in order to ameliorate this concern is for the authors to also discuss the case of scalar models in $d=3-\varepsilon$, where the scalar potential involves the sixth power of the scalar field. In that case, the authors' argument in section 4 does not appear to go through in its current form, although there might be refinements. The case of $d=6-\varepsilon$ could also be discussed, where the scalar potential is cubic in the field and again the authors' argument does not appear sufficient to prove a statement similar to $d=4-\varepsilon$ in its current form. These cases could be discussed briefly in the conclusion and outlook section.
Requested changes
1- Discuss $d=3-\varepsilon$ case
2- Discuss $d=6-\varepsilon$ case