# Isospin asymmetry in holographic baryonic matter

### Submission summary

 As Contributors: Nicolas Kovensky Preprint link: scipost_202105_00024v1 Date submitted: 2021-05-17 19:22 Submitted by: Kovensky, Nicolas Submitted to: SciPost Physics Academic field: Physics Specialties: High-Energy Physics - Theory High-Energy Physics - Phenomenology Nuclear Physics - Theory Approach: Theoretical

### Abstract

We study baryonic matter with isospin asymmetry, including fully dynamically its interplay with pion condensation. To this end, we employ the holographic Witten-Sakai-Sugimoto model and the so-called homogeneous ansatz for the gauge fields in the bulk to describe baryonic matter. Within the confined geometry and restricting ourselves to the chiral limit, we map out the phase structure in the presence of baryon and isospin chemical potentials, showing that for sufficiently large chemical potentials condensed pions and isospin-asymmetric baryonic matter coexist. We also present first results of the same approach in the deconfined geometry and demonstrate that this case, albeit technically more involved, is better suited for comparisons with and predictions for real-world QCD. Our study lays the ground for future improved holographic studies aiming towards a realistic description of charge neutral, beta-equilibrated matter in compact stars, and also for more refined comparisons with lattice studies at nonzero isospin chemical potential.

###### Current status:
Has been resubmitted

### Submission & Refereeing History

Resubmission 2105.03218v2 on 13 July 2021

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Submission scipost_202105_00024v1 on 17 May 2021

## Reports on this Submission

### Anonymous Report 2 on 2021-7-9 (Invited Report)

• Cite as: Anonymous, Report on arXiv:scipost_202105_00024v1, delivered 2021-07-09, doi: 10.21468/SciPost.Report.3218

### Report

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.

• validity: high
• significance: high
• originality: high
• clarity: top
• formatting: perfect
• grammar: perfect

### Anonymous Report 1 on 2021-7-4 (Invited Report)

• Cite as: Anonymous, Report on arXiv:scipost_202105_00024v1, delivered 2021-07-04, doi: 10.21468/SciPost.Report.3183

### Strengths

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

### Weaknesses

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

### Report

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.

### Requested changes

None.

• validity: high
• significance: good
• originality: high
• clarity: high
• formatting: excellent
• grammar: perfect