Non-Abelian Gauge Theories with Composite Fields in the Background Field Method

Round 1

Reviewer 1 Report

In this work, the authors examine non-abelian gauge theories with composite fields in the background field method.

Although the manuscript is very technical and very difficult to follow without checking all the calculations (which I only have done at some places), the authors have made an important effort both at the end of the introduction and also at the end of the paper by remarking the problems they are able to solve within their techniques. I think that, with this guidance, the reader interested in these aspects of QFT may follow the authors calculations and arguments, which I consider to be valuable for the  specialized community. Therefore, I recommend publication.

Author Response

We are thankful to the Reviewer for the positive comments for the paper.
Of course, we agree that the details of some results seem to be technical. However, we provide the correctness of all steps   when make the calculations to get exact answers with required accuracy.
We hope that we were sufficiently close with optimal presentation. 

Reviewer 2 Report

This paper presents a detailed BRST-based analysis of non-Abelian gauge theories with composite fields and  background terms, with applications to interesting models such as the Gribov-Zwanziger action and a 2-dimensional gravity theory. Important topics such as effective actions and gauge covariance are discussed. While the presentation is very technical, this lies in the nature of the topic and its considerable generality.

The only suggestion I have is that the introduction could motivate the analysis more carefully. It starts with a dense enumeration of previous papers, which does show the relevance but makes it difficult to judge the background for readers not directly familiar with the context.

Author Response

We are thankful to the Reviewer for the positive and critical comments for the paper.
Of course, we agree that the details of some results seem to be technical. However, we provide the correctness of all steps   when make the calculations to get exact answers with required accuracy.
We hope that we were sufficiently close with optimal presentation. 

We agree with Reviewer's remarks, namely, 

"The only suggestion I have is that the introduction could  motivate the analysis more carefully. It starts with a dense  enumeration of previous papers, which does show  the relevance but makes it is difficult to judge the background  for readers not directly familiar with the context."    The modifications in the revised manuscript have affected the following:   1) Introduction, 2) Acknowledgments, 3) Literature references   Specifically, regarding items (1), (2), (3),    1) Paragraphs 1, 2 have been modified, with the changes highlighted  by boldface. Paragraph 3 has been added and indicated by boldface. In paragraph 4: the phrase "in the presence of both composite  and background fields" has been removed as unnecessarily repetitive.   2) The first sentence has been replaced and accordingly highlighted by boldface.   3) Some of the literature references have been rearranged to address  the modifications affecting item (1) and generally suit their order  of appearance in the body of the manuscript more adequately.    We would like to express our gratitude to the Referee for the criticism which has been quite helpful in improving the manuscript.