Confinement Potential in a Soft-Wall Holographic Model with a Hydrogen-like Spectrum
Round 1
Reviewer 1 Report
Dear Editor,
Universe
The manuscript "Confinement Potential in Soft Wall Holographic Model with Linear Dilaton" is clearly written with a well defined problem to tackle. This is an interesting subject related to the fundamental problem of confinement in QCD.
The calculation is presented with many intermediate steps making it easy to follow every advancement in the text.
This work is strongly inspired by Ref. 5 by Andreev and Zakharov, where the authors obtain a confinement potential from a deformed AdS metric with a quadratic exponential factor, resembling the form of the quadratic dilation of the original soft wall model, presented in Ref. 2.
In the present manuscript the ideia of Ref. 5 is reproduced but this time with a linear exponential factor in the AdS metric. This allows a deduction of many analytic steps.
However, it should be noticed that, after Ref. 5, at least two other works deal with this problem:
A. The Cornell Potential from General Geometries in AdS/QCD, C.D. White, PLB 652 (2007) 79;
B. Quark-Antiquark Potential from a Deformed AdS/QCD, Rodrigo C. L. Bruni et al., AHEP (2019) 1901659.
In Ref. A above, a general deduction of the Cornell (confining) potential is presented for general AdS deformed metrics.
In Ref. B above, a deduction of the confining potential was presented for AdS metrics deformed by a factor exp{z^n}, which contains as particular cases Ref. 5 (with n=2) and the present manuscript with n=1.
Anyway, I think that the present manuscript contribute to the advancement of the subject. So, if it is rewritten to take into account Refs. A and B above properly, it can be published in the Universe.
Author Response
We cited 8 new papers in which the problem was also addressed (see Refs. [7-14]), including the references A and B indicated by the reviewer. The 3rd paragraph in Introduction is extended, the content of work A is briefly mentioned. Also we added a new paragraph with discussion of some interrelations between our analysis and analysis of Ref. B – the last paragraph of Section 4.2.
The title and abstract were partly changed to give a more precise account for the content of the paper
Reviewer 2 Report
The authors studied the holographic Soft Wall model with a linear dilaton, and found that it could result in a Cornell potential. The interesting point was that the authors discussed that the Soft Wall model with the positive dilation model did not possess the Regge spectrum. As an example the authors calculated a scalar Soft Wall model with linear dilaton, and found that the model is Hydrogen-like. Another important point I think was that the authors argued that infinite number of bottom-up models which did not have the Regge spectrum but do have the property of linear confinement, which could be computed from the Wilson loops. Totally, I think this is an interesting paper in the holographic area, which may provide new insights to this field. I suggest to accept this paper.
Author Response
The English was corrected in several places
Reviewer 3 Report
The soft wall holographic model is a semiphenomenological model for quark confinement in QCD. It is not uniquely specified and the several papers written on the topic reflect this, there are many different ways of specifying the soft wall. Here one introduces for this purpose a linear exponential function (to be contrasted with a Gaussian, for example) and computes various consequences of this choice. Other workers in the field may find these results worth consulting and, although this is not the final word on the topic (none is), I think this article deserves being published. The list of references is not exhaustive but probably adequate.
Author Response
The English was corrected in several places.
Round 2
Reviewer 1 Report
The present form of the manuscript has been improved after the revision of the first version submitted to Universe.
However, I still think that the authors should give credit to the appropriate authors, especially in section 2 of the manuscript where the models considered are not new. Naturally, in the following sections, there is new material.
Author Response
We agree, section 2 contained no references, we added several ones. Also the 3rd paragraph in Introduction is a bit extended with a discussion of previous results. Found misprints are corrected.
