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Dilaton in scalar QFT: a no-go theorem in 4-epsilon and 3-epsilon dimensions
by Daniel Nogradi, Balint Ozsvath
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Submission summary
| Authors (as registered SciPost users): | Daniel Nogradi |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202201_00001v3 (pdf) |
| Date submitted: | 2022-04-08 18:56 |
| 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. The arguments apply to $\phi^6$ theory in $3-\varepsilon$ dimensions as well.
Author comments upon resubmission
List of changes
The title of the paper is extended and now is
"Dilaton in scalar QFT: a no-go theorem in 4-epsilon and 3-epsilon dimensions"
The abstract got an additional sentence "The arguments apply to phi^6 theory in 3-epsilon dimensions as well." too.
In section 1 an additional paragraph plus an additional sentence was added on the 3-epsilon phi^6 case.
Section 5 is new and is dedicated to the 3-epsilon dimensional phi^6 case.
The conclusion section (Section 6) is extended by 2 paragraphs, one about the 3-epsilon dimensional phi^6 case and a brief mention of the 6-epsilon dimensional phi^3 case.
We would like to thank the referee again for bringing up the other dimensions for discussion, we feel the additional results on phi^6 in 3-epsilon dimensions was a worthwhile addition.
The other referee had the following questions:
"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."
Fishnet CFT's are examples of non-unitary theories with a dilaton, which was already discussed in the introduction (Section 1). This construction can be thought of as the large-N limit of gamma-deformed N=4 SUSY Yang-Mills theory at strong deformation and weak coupling. The resulting theory is renormalizable and non-unitary and contains a dilaton. The discussion is also present in the Conclusion section.
We believe the addtions and modifications improved our paper and hence would like to thank both referees for their input.
In order to ease the next round of review of our manuscript we highlighted the added text in red.
Current status:
Reports on this Submission
Report #1 by Andreas Stergiou (Referee 1) on 2022-4-14 (Invited Report)
Report
The authors' additions strengthen their manuscript significantly. This manuscript is well-written and contains enough new results to be published in SciPost Physics. I thus recommend publication.