Holographic Non-Abelian Flavour Symmetry Breaking

Round 1

Reviewer 1 Report

The paper reports on interesting research work, on a topical subject, and, to the best of my understanding, is scientifically sound, hence it deserves publication.

The presentation should be improved: I expect that some additional proofreading and editorial work would easily allow the authors to improve on the many, small but distracting, presentation issues in the manuscript, that in the present form at times take attention away from its interesting content.

 

I would recommend to improve the quality of the presentation: the text contains many typos and grammatical errors (including the occasional appearance of "it's" in place of "its", for example, and such phrases as "quark's representation...",  or  "fluctuations' equations", or "The general case is if one has..." or "...follow a new story that was..." and similar), is missing essential punctuation (many equations are written without punctuation, for instance, but commas are missing also in the text, and there is an example of "Note, that..."), introduces inconsistencies in the notation ($N$ and $N_c$ alternate, early in the text, for example). Some of the equations in the Appendix are not integrated into the narrative of the text. In general terms, the English of the exposition at times does not live up to the high standards expected on the basis of the established International reputation of the authors, and although taken individually these are all rather minor flaws, I think it is in the authors' best interest to improve upon them.

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

 

The authors present a well-written and interesting study of non-Abelian flavour symmetry breaking using the holographic model. The authors clearly articulate their motivation for studying this problem and comprehensively introduce the relevant works, concepts, and models.

I appreciate the clarity and organized the paper, which makes it easy to follow the authors’ arguments and understand the key results. The authors, first review the key ingredients in the top-down D3/probe D7-brane model, followed by a clear and concise description of the bottom-up non-abelian dynamic AdS/QCD theoretical framework and the main equations used in their analysis. By carefully choosing the potential which breaks the dynamical chiral symmetry of the model. The authors extract the meson masses from the resulting equation of motions, that are comparable with the real QCD masses. The results are presented in a logical and systematic way, with detailed explanations and discussions of the physical implications.

One of the strengths of the paper is the use of holographic techniques to study the non-Abelian flavour symmetry breaking. The authors provide a detailed explanation of the AdS/CFT correspondence and its relevance to the current work, which demonstrates their understanding of the theoretical framework and its implications. The holographic approach also allows for a clear interpretation of the results in terms of the dual gravity theory, which is a valuable contribution to the field.

However, I have a few suggestions for improvement. Firstly, it would be helpful to provide more details on the numerical methods used in the analysis of Eq(3.19) and the subsequent plot of Fig 4, such as the boundary conditions and the convergence tests. This would help readers to better understand the numerical results and their reliability. Secondly, the mass of eta prime deviates from its QCD real mass by 19%. Does this framework capable of including the chiral anomaly to explicitly confirm this discrepancy? This is not required here, but just for the self-completeness of this framework.

Overall, I find the paper to be well-written and well-organized, with interesting and valuable results. I recommend the publication of this paper after addressing the above suggestions. 

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

The Authors study a bottom-up holographic model describing explicit and spontaneous symmetry breaking of non-abelian flavour symmetries. Symmetry breaking on the boundary becomes a Higgs mechanism in the bulk, in which quark masses and chiral condensate are generated as boundary conditions on the vev of the scalar field. An anomalous dimension for the scalar field is introduced. Three main cases are analysed: two quarks with equal masses, two quarks with different masses, two quarks with equal masses (up and down) plus one quark with higher mass (strange). The mass spectrum of some light mesons is computed, finding values in good agreement with the observed spectrum in the three flavour case.

The relevance of the manuscript is based on the description of light meson spectroscopy in holographic models with N_f=2+1 flavours, providing an advancement of the current knowledge of such methods, so the manuscript is worth being published.

The following points should be discussed before the publication.

1) It is not clear the role of the dilaton. It is introduced in Eq. (2.2) but then it disappears from the equations. Has it been set to zero? Is $\Phi$ in Eq. (2.9) the dilaton?

2) In section 4, in order to describe the QCD vacuum, the Authors introduce a scalar field $X$ containing the chiral condensate. However, since the field $X$ is numerically determined, it is not possible to explicitly recognise a chiral condensate in the solution, if it is related to or independent of the quark mass, and what is its value. The Authors should add some comments about this quantity, showing it is indeed different from zero and possibly underlying any interesting feature it gets in this model.

3) The Authors should explain why they have adopted the boundary conditions in Eq. (4.14) for $L_i$ or at least provide a reference where the meaning of such a choice is shown.

4) The last sentence of section 4.2 needs to be clarified.

5) Is a square missing in the second term of Eq. (4.35)? Moreover, is a square missing in the double trace term in the paragraph after Eq. (4.35)?

6) In the three discussed cases, how have the values of the quark masses been chosen?

7) In Table III the masses of radial excitations of pseudoscalar states have not been indicated. It would be interesting to know their value in this model since a drawback of some holographic models is that it is not possible to reproduce the experimental masses of excited pseudoscalar mesons. In particular, it is not possible to match these quantities and the pion decay constant with their experimental values using the same set of parameters.

Author Response

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Reviewer 4 Report

The paper describes a bottom-up holographic model for spontaneous and explicit breaking of flavour symmetries inspired by the top-down approach. This topic is very interesting in holography and may bring some insights to the problem of dynamical mass generation in QCD. The paper is very well written and the results seem to be consistent. I recommend the paper for publication in Universe.  

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 3 Report

The Authors have properly answered to the issues in the previous report. I recommend the paper for publication.