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Soliton confinement in the double sine-Gordon model
by Sergei Rutkevich
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Sergei Rutkevich |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2311.07303v2 (pdf) |
| Date accepted: | 2024-02-01 |
| Date submitted: | 2023-12-27 11:27 |
| Submitted by: | Rutkevich, Sergei |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
The double sine-Gordon field theory in the weak confinement regime is studied. It represents the small non-integrable deformation of the standard sine-Gordon model caused by the cosine perturbation with the frequency reduced by the factor of 2. This perturbation leads to the confinement of the sine-Gordon solitons, which become coupled into the 'meson' bound states. We classify the meson states in the weak confinement regime, and obtain three asymptotic expansions for their masses, which can be used in different regions of the model parameters. It is shown, that the sine-Gordon breathers, slightly deformed by the perturbation term, transform into the mesons upon increase of the sine-Gordon coupling constant.
Author comments upon resubmission
I am thankful to the Referees for their reviews, remarks and suggestions, which were very helpful.
I have accounted Referee's suggestions in the revised version of the manuscript.
Sincerely yours,
Sergei Rutkevich
List of changes
Numbering of pages, equations and references in the list of changes correspond to the revised version of the manuscript.
1. Page 2, Eq. (1). I replaced 8π by 16π in the integrand in the right-hand side.
2. Page 4. The following footnote is added to Line 4:
*The origin of the O(2) isotopic symmetry of the sG model was discussed in [13] in page 268.
3. Pages 5,6. The text between Eqs. (15c) and (21) [Eq. (18) in the original version] is modified. I describe
here in more details the degeneracy of the scattering amplitudes at the reflectioless points.
4. Page 10. The in-line equation in this page is transformed into the numbered one, Eq. (46).
5. Pages 11, 12. Following the recommendation of the Referee, the last paragraph of Section 3 in the
original version of the manuscript is modified and extended, in order to provide more details for the reader.
6. Page 15. O(ρ^{-2}) in the first non-numbered formula in this page is replaced by O(ρ^{-3}).
7. Page 15. The last term in the third line in Eq. (83) differs from that in the original version, see Eq. (78) there.
The new form of this term is more informative, thought the previous one was also correct.
8. Page 16. One paragraph, that includes the new Eq. (87), is added:
The linear in λ correction ... reproduced by our formula (85).
9. Page 16. The last term in the third line in Eq. (90) is modified similarly to that in Eq. (83).
10. Page 18. Figures in this page are slightly increased in size.
11. Page 21. The green dashed curve is added in Figure 6, following the Referee’s recommendation.
The description of this curve is added into the figure caption, and also into the first and second paragraphs in Page 21.
12. Page 23. Two sentences are added in the first paragraph:
Namely, the semiclassical expansion ... modified low-energy expansions (81) and (88).
13. Page 29. The reference
[13] A. B. Zamolodchikov and Al. B. Zamolodchikov, Factorized S-matrices ...
is added into the list of references.
Besides, several types and grammar mistakes were corrected.
Published as SciPost Phys. 16, 042 (2024)
Reports on this Submission
Report #2 by Sergei Lukyanov (Referee 4) on 2024-1-16 (Invited Report)
Report
In my previous report I recommended the paper of Sergei Rutkevic for publication. The most important change in the revised version is formula (87) for the form factor perturbation theory. Its prediction is plotted in Figure 6. I think this is a nice addition to the work. As before, I believe the manuscript is worthy to be published.
Report
The author answered my questions (if not directly but through the modifications of the manuscript), and implemented the suggested changes.
(Note that my question about the original Eq. (77) was incorrect.)
I recommend publication of the paper in SciPost Physics.