SciPost Submission Page
Symmetry energy in holographic QCD
by Lorenzo Bartolini, Sven Bjarke Gudnason
Submission summary
| Authors (as registered SciPost users): | Sven Bjarke Gudnason |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202312_00005v1 (pdf) |
| Date submitted: | 2023-12-02 07:44 |
| Submitted by: | Gudnason, Sven Bjarke |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Phenomenological |
Abstract
We study the symmetry energy (SE), an important quantity in nuclear physics, in the Witten-Sakai-Sugimoto model and in a much simpler hard-wall model of holographic QCD. The SE is the energy contribution to the nucleus due to having an unequal number of neutrons and protons. Using a homogeneous Ansatz representing smeared instantons and quantizing their isospin, we extract the SE and the proton fraction assuming charge neutrality and beta-equilibrium, using quantization of the isospin zeromode. We also show the equivalence between our method adapted from solitons and the usual way of the isospin controlled by a chemical potential at the holographic boundary. We find that the SE can be well described in the WSS model if we allow for a larger 't Hooft coupling and lower Kaluza-Klein scale than is normally used in phenomenological fits, passing all experimental constraints and is compatible with results from nuclear physics at low densities.
Current status:
Reports on this Submission
Strengths
The paper has a clear goal, the procedure is carefully explained, and the results obtained and comparisons with previous publications are clearly discussed.
Weaknesses
Given the equivalence with previous works discussed briefly in the main text and in detail in appendix A (up to some details) the paper would benefit from a more explicit discussion of the motivation for carrying out the present computation, not only from the technical point of view but also in view of possible future directions of investigation.
Report
In holographic QCD models baryons are usually understood as gauge instantons in the bulk. However, the difficulty in handling many instanton systems requires the use of some approximations when using this formalism to describe dense QCD-like matter. The present manuscript considers the homogeneous Ansatz routinely used in this context for the WSS and HW models, and successfully carries out an analog of the isospin quantization procedure perfomed originally for the single-instanton in the WSS model (and also in the Skyrme model). The analysis is valid at small isospin chemical potential, which is enough to compute the symmetry energy, roughly speaking around saturation density, that is, in the regime relevant for Neutron Star matter.
Appart from a few minor points, detailed below, in my opinion the paper is technically interesting, and timely, as the application of holographic methods to Neutron Star physics has led to important results in recent years. Hence, I believe it should eventually be published in SciPost Physics.
My only important suggestions for improving the final version are the following:
- The authors mention in the introduction, main text, and show in appendix A, that the method used here is basically equivalent to that of Ref [35]. The only two differences are (1) the choice of the Nc scaling in the definition of the isospin chemical potential and the symmetry energy, and (2) the correct inclusion of the abelian spatial components, which were originally ignored in [35] (although the authors might comment on the discussion given in Ref [54] regarding this point, namely the impact of this approximation on the phase diagram of the model). However, when discussing the results for the symmetry energy and proton fraction in Secs 4 and 5, the authors say that they are much closer to the phenomenological values. I believe it should be clarified how much of this improvement actually relies on the conventional Nc scaling, and how much is due to the improvement of the Ansatz for the Abelian gauge fields.
- Besides the computation of a more realistic symmetry energy and proton fraction (and especially if the improvement is mostly due to the Nc scaling), I believe the authors should clarify what is the main advantage of carrying out the computation in this way. For instance, what is the impact for future applications to Neutron Stars? How would those hypothetical results compare with those from other holographic NS models, such as those based on VQCD? What other applications would benefit from the quantization analysis?
- In the discussion section, it is said that the holographic popcorn transition is "already taken into account", but this is the first mention of it. I believe this comment is too vague. If it is part of the computation, it should be explained in the main text when it enters, and it's impact should be discussed, as well as it's comparison with non-holographic models, quarkyonic matter, etc.
Requested changes
Besides addressing the questions raised in the above report, here is a list of minor points the authors should consider:
- At the beginning of section 2, it is said that at low energies both models are described by gauge theories on AdS5, but then the metric for the WSS model is different. I understand what the authors mean, but the presentation seems a bit confusing.
- The use of the coordinate "z" in both cases has its advantages, but it is a bit confusing that in the HW case there is a scale "L" for the AdS radius, but in the WSS model "z" is dimensionless. Perhaps this could be clarified as well.
- In footnote 3 one could also consider citing recent papers where the effect of the quark mass on the phase diagram of the system was considered.
- Below Eqs (35)-(38) it would be useful to explain more carefully (at least in words) why some terms quadratic in \chi are important while others are ignored.
- It would be interesting to discuss in more detail what happens with the equivalence discussed in App. A for larger values of the isospin chemical potential, and how it could affect studies of the phase diagram and of Neutron Stars within these models.
Recommendation
Ask for minor revision