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Phases of cold holographic QCD: baryons, pions and rho mesons
by Nicolas Kovensky, Aaron Poole, Andreas Schmitt
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Submission summary
| Authors (as registered SciPost users): | Nicolas Kovensky · Aaron Poole |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202303_00007v1 (pdf) |
| Date submitted: | 2023-03-07 11:32 |
| Submitted by: | Kovensky, Nicolas |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We improve the holographic description of isospin-asymmetric baryonic matter within the Witten-Sakai-Sugimoto model by accounting for a realistic pion mass, computing the pion condensate dynamically, and including rho meson condensation by allowing the gauge field in the bulk to be anisotropic. This description takes into account the coexistence of baryonic matter with pion and rho meson condensates. Our main result is the zero-temperature phase diagram in the plane of baryon and isospin chemical potentials. We find that the effective pion mass in the baryonic medium increases with baryon density and that, as a consequence, there is no pion condensation in neutron-star matter. Our improved description also predicts that baryons are disfavored at low baryon chemical potentials even for arbitrarily large isospin chemical potential. Instead, rho meson condensation sets in on top of the pion condensate at an isospin chemical potential of about $9.4\, m_\pi$. We further observe a highly non-monotonic phase boundary regarding the disappearance of pion condensation beyond about ten times nuclear saturation density.
Current status:
Reports on this Submission
Report #1 by Anonymous (Referee 2) on 2023-5-17 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202303_00007v1, delivered 2023-05-17, doi: 10.21468/SciPost.Report.7204
Report
The paper analyzes in details the phase diagram in the baryon and isospin chemical potential plane of the holographic QCD model of Sakai and Sugimoto in the confined phase. The paper is very well written, the computations and their implications are clearly stated and commented. A number of results are new and interesting. I believe they are worth to be published in SciPost.
Nevertheless, I believe the presentation could be more reader-friendly if the following points are considered.
1. The authors discuss in details some limitations of their approach, for example the use of a diagonal ansatz for the gauge fields: they find out that it is reasonable to assume that this crude approximation gives a qualitatively correct phase diagram - I tend to agree with this statement. Nevertheless, as far as I can see, this issue does not appear anywhere in the "Introduction and conclusions" section. Being the latter quite long, and being absent a concluding section, mentioning in the Introduction the used approximation would be fair to the reader.
2. I would also appreciate a line or two in the Introduction section on the dependence of the phase diagram on the parameter \lambda, discussed in section 5.5. In fact, the phase diagram of figure 1 is calculated for a relatively small value of \lambda (smaller than 8). For larger values, as can be seen in figure 7, the phase diagram presents some qualitative difference. Since the gravity computations are reliable in the large \lambda limit, this could point towards the fact that some features of the phase diagram in figure 1 could change by including 1/\lambda corrections.
Report #2 by Anonymous (Referee 1) on 2023-5-17 (Invited Report)
- Cite as: Anonymous, Report on arXiv:scipost_202303_00007v1, delivered 2023-05-17, doi: 10.21468/SciPost.Report.7205
Report
This manuscript analyzes in detail the phase structure of QCD at finite baryon and isospin chemical potentials by employing the holographic Witten-Sakai-Sugimoto model. This study is continuation of earlier work in this topic. The authors extend earlier studies by considering the effects of finite pion mass and the effect of rho meson condensation, which leads to a complex phase diagram containing several interesting new results. The study is probably the most extensive exploration of the phases of holographic QCD at finite isospin chemical potential. It is also well motivated, as not so much is known about the phase structure of QCD at high densities from first principle QCD analysis, and some of the phases are relevant for neutron star physics. Due to the complexity of the phase structure the article is quite technical, but the details are explained very well. Therefore I think that the manuscript clearly passes the acceptance criteria for SciPost Physics. I have only minor comments and questions that the authors should check.
On page 10 below Eq. (25), it is written "...the non-zero field strengths are...", but the expressions which are referred to here are not field strengths but gauge field components.
On page 11 below Eq. (30), "Subtracting this vacuum contribution, the factor from the Nambu-Goto action is 1." I did not understand this comment, do the authors mean that $e^{-S_{NG}}$ evaluates to one?
On page 17, the authors discuss the equations of motion. They refer to the "full" equations of motion in Eqs. (29). However in
Eq. (50) an approximate Lagrangian density was introduced. Do I understand correctly that the equations of motion on page 17 match with the "diagonal" components of Eqs. (29), and are also consistent with the approximate action of Eq. (50)?
On page 18 below Eq. (67) the authors comment "This result ... does assume its derivative to be discontinuous." But if $h$ is odd, as far as I can see the derivative is, in fact, continuous (while the function itself is discontinuous).
In section 4.5 the authors discuss the $\beta$-equilibrium and charge neutrality conditions for neutron star matter. Maybe it would be a good idea to remind at the end of this section what they are used for, as at the moment the text ends rather abruptly. Do I understand correctly that the neutron star matter conditions are only used to draw the blue line in Fig. 1, but are otherwise irrelevant for the phase diagram?