# Talk:Novikov-Shifman-Vainshtein-Zakharov beta function

## Reviewer B

I think that this "living review" would be a nice opportunity for a definitive discussion on the origin of the denominator of the NSVZ beta function, which gave rise to a lot of literature and debate.

Moreover, related to this issue, I believe that it would be useful a remark on the relation between "holomorphic" and "canonical" gauge coupling constant, which originates the well known puzzle concerning the absence of evolution of the "canonical" gauge coupling constant below a certain scale.

Under this respect, indeed, the pole of the NSVZ beta function seems to be just a sign of the failure of \alpha as a coupling constant at low energies.

Finally, the Author uses both \alpha and *g* for the gauge coupling constant. Does He refer to the same coupling constant ?

## Author's answer

1) Refereee A He made two (almost identical) comments in the text. I do not think these comments are relevant, since the referee A seemingly does not realize that at this point I discuss the zero modes in the instanton background, and only matter fermions (not bosons!) have these zero modes. Matter spin-zero fields have no zero modes in the instanton. To make this aspect absolutely clear I added " in the instanton background" in the text, and erased the comments of referee A.

2) As for the referee B, I added the definition of \alpha in terms of g^2. It seems to me that his other proposals go way beyond the scope of an encyclopedic article. He suggests a thorough discussion of the denominator of the NSVZ beta function since, allegedly, " the question is not yet settled in the literature". First, I do not think it is not settled; second, Scholarpedia is definitely NOT an appropriate forum for discussing and debating nuances.

The distinction between the canonic and holomorphic constants is mentioned at the end of section "History and theoretical basis". I believe that the reference given there is sufficient for an encyclopedic article. After all, this is NOT a comprehensive review. The goals of the former and the latter are different.

### Reviewer B reply to Author's point 2 above

Contrarily to the Author's opinion, I believe that an encyclopedic article, more that a regular journal article, should give an as much as possible comprehensive review, which is definitely not the case under consideration. But the Author for three times in his reply explicitly says that Scholarpedia is not worth an inclusive study, so he is coherent, under this respect.

My opinion is that the Author's contribution does not fit the Scholarpedia "Aims and policy" which I read in http://www.scholarpedia.org/article/Scholarpedia#Aims_and_policy. In particular it does not appear to me a "useful encyclopedic reference for scholars of different levels".