Thickness and Color Structure of Center Vortices in Gluonic SU(2) QCD

Round 1

Reviewer 1 Report

In the manuscript the authors analyze the thickness and color structure of center vortices in SU(2) quantum chromodynamics. Their findings hint at a vanishing thickness in the continuum limit and a longitudinal color structure of the vortex surface. I believe that the results are significant enough to warrant publication.

Concerning the style, the manuscript is well written and organized. In my opinion, the Introduction and parts of the paper, however, are quite technical and sometimes difficult to read. They could be held a bit more general and include more explanations. This would arouse more interest on this topic, also for theorists who do not work directly on this interesting topic, and as a consequence the paper would have a broader impact. Apart from some suggestions for improvement (see below) I can recommend the paper for publication in the journal MDPI-Particles.

Specific questions and some further suggestions for improvement:

-Maybe the authors could comment on the physical consequence of a vanishing thickness of the center vortices in the continuum limit in more detail. They might want to include a sentence or 2 on this in the Discussion section of the paper.

-Do the authors have a rough idea how difficult a generalization to real SU(3)-QCD would be and how far they are away to reach this aim?

-the parameter \beta first appears in Table 1 but is not introduced and only referred to to references.

-line 49: it should read “...is not necessarily...”

-line 51: it should read“...require much more statistics...”

-line 101 it should read “...requires more statistics.”

-Eq. (9): it should be O(a^3/fm^3)

Author Response

Dear reviewer,

As this is the first publication presenting the algorithms for detecting thick Center vortices we can not reduce the technical details much more. A more general introduction into the topic would indeed be very favorable, but goes beyond the scope of this publication.

The discussion is now supplemented by additional comments concerning the physical consequence of a vanishing vortex thickness (lines 120 to 124). It is of interest, if a vortex with thickness vanishing in the continuums limit reproduces Casimir scaling of the string tension.

The generalization to SU(3) is discussed in more detail (lines 134 to 142) and the inverse coupling \beta is introduced earlier in the introduction (first paragraph).

The modifications of the gauge fixing procedure are now presented in a bit more detail now (lines 12 to 15) and in the discussion we mention what improvements can be reached by collecting more data (lines 128 to 132).

Thank you very much for the constructive feedback which helped to improve the publication!

With best regards,
Rudolf Golubich

Reviewer 2 Report

The understanding of the QCD vacuum is an important problem. The authors study it via the Wilson action with center vortices in the non-Abelian group SU(2). The computation in SU(3) will be as stated by the authors very interesting. The study merits publication on the result of the vanishing thickness of the center vortices.

The authors may consider the following minor comments:

1) Explain gauge fixing procedure in the introduction. What is the procedure/measure of the "maximal center gauge preserving non-trivial center regions"?

2) Explain how much statistical improvement can be expected by which data (p10 discussion).

3) Add reference in the introduction to the previous on topic SU(2) study hep-lat/9610005

4) Fix typo: monopols -> monopoles

Author Response

Dear reviewer,

The modifications of the gauge fixing procedure are now presented in a bit more detail now (lines 12 to 16) and in the discussion we mention what improvements can be reached by collecting more data (lines 127 to 132).

The discussion is now supplemented by additional comments concerning the physical consequence of a vanishing vortex thickness (lines 120 to 124) and also the generalization to SU(3) is discussed in more detail (lines 136 to 146) and the inverse coupling \beta is introduced earlier in the introduction (first paragraph).

Also the reference you mentioned is listed.

Thank you very much for the constructive feedback!

With best regards,
Rudolf Golubich