Isospin asymmetry in holographic baryonic matter

The authors carry out an extensive and detailed study of isospin asymmetry in the baryonic phases of the holographic Witten-Sakai-Sugimoto model. As far as I can see this topic has not been addressed in earlier literature in any holographic model. The manuscript is very well written, contains several interesting new results, and opens possibilities for future studies. The results their connections to QCD phenomenology, and connections to earlier literature are discussed thoroughly. The authors use various approximations and some results clearly disagree with QCD, but the reasons for these are explained carefully. The subject is also topical due to the recent progress in neutron star physics. Therefore I think it is clear that the manuscript should be accepted for publication in SciPost Physics. I only have minor questions and comments.


In Eq. (78) the authors introduce a square root action for the homogeneous nuclear matter in the deconfined phase. This action is well motivated, but would it make sense to also consider the same or similar action in the confined phase? And if it would, do you expect that it would change any of the results significantly?

The authors might consider extending the review of Ref. [52] in Sec. 2.4 by adding more details, if they think this could improve clarity. However this is optional; the current discussion is also ok.

In the last paragraph on page 4, what exactly do the authors mean by "the baryonic spectrum becomes continuous in isospin space"?

On page 29, above Eq. (77), the authors write that "Truncations of the resulting infinite series at $\mathcal{O}(F^2)$ or $\mathcal{O}(F^4)$ are possible, but also lead to a relatively complicated action..." Is this clear for the $\mathcal{O}(F^2)$ truncation also? I would have expected that the $\mathcal{O}(F^2)$ truncation just gives the YM approximation also in this case, which is perhaps not that complicated.

On page 32, after Eq. (92), the authors say that the connection between $\hat a_c$ and the baryon mass was pointed our in Ref. [9]. Wasn't this or a similar relation already demonstrated in the earlier Ref. [50]?

On page 34 after Eq. (106), there's a comment "... which determines the
boundary conditions $h(u_c) = h_c$ and $a_0(\infty)$, respectively." Here "$a_0(\infty)$" is not a condition, perhaps something is missing?

In the last paragraph on page 37, I found the sentence "In a more realistic scenario, where..." difficult to understand. Maybe it should be reworded.

1-The authors give a thorough analysis of baryonic matter in the presence of both isospin and baryon chemical potentials in a holographic setting.

None. All weaknesses in the analysis are mentioned in the paper and addressed satisfactorily.

The authors solve an important problem in the study of the matter that makes up neutron stars. I therefore found the paper very interesting, and recommend the paper for publication in SciPost Physics.

None.