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Dilaton in scalar QFT: a no-go theorem
by Daniel Nogradi, Balint Ozsvath
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Submission summary
| Authors (as registered SciPost users): | Daniel Nogradi |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202112_00031v1 (pdf) |
| Date submitted: | 2021-12-13 18:46 |
| 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. Even though at leading order it is possible to construct models which give rise to spontaneous scale invariance breaking and indeed a massless dilaton can be identified, it is shown that the particular form of the running coupling $\beta$-function spoils this property already at 1-loop. As a result spontaneous scale symmetry breaking can not occur in renormalizable, unitary 4 dimensional scalar QFT.
Author comments upon resubmission
List of changes
The comments of the two referees largely pointed in the same direction, namely that the main point is not the masslessness of the dilaton, but rather the lack of spontaneous scale symmetry breaking. We completely agree and have revised the wording in several places in the manuscript. We have already noted that of course anomalous symmetry breaking is present and the main question in the manuscript is whether spontaneous breaking can also take place along the anomalous breaking or not. In several instances this was formulated as whether an exactly massless dilaton exists or not. This wording was not correct and potentially misleading, hence we clarified everywhere that we are after spontaneous scale symmetry breaking (and the main result is the lack thereof) and not a massless dilaton. Because of the anomaly the dilaton could at best be light or approximately massless only. The last sentence of the abstract is modified as well.
The suggested very relevant references were added and we'd like to thank the referees again for pointing our attention to these works.