Renormalization of the R-charge?

Question

In general I would like to know as to known or what is/are the standard references about R-charge renormalization in supersymmetric theories. When does it do so and what is expected or known to be interesting.

• A little more specifically I want to know whether something is particularly special if the R-charge of the scalar chiral superfield in some theory is seen to be flowing to values greater than 1/2 under the flow.

• And if the R-charge of the scalar chiral superfield is flowing to values less than half then what does it physically imply? I have at times seen a vague argument along this line that if it is flowing to 0 asymptotically then that means that the theory is developing a continuum spectrum in that limit - which is supposed to be more surprising if the theory was defined on a compact space(-time?) to start with. But I don't understand the above argument any much more and would like to know of precise statements/derivations/references - and hopefully pedagogic ones from where a beginner in the field can learn!

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Comments

user6818 - If you configure your account with a proper username and accept (where applicable) a few more answers to your previous questions, then you'll be more likely to get replies and people will be more willing to put time into composing those replies...

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@Simon As you can see from my comments to the answers to the few questions that I have asked - there haven't been addressing my question. I am hoping that there will be satisfying answers which I can happily "accept". Or may be I will announce a bounty.

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That's the problem with the stackexchange model and theoretical physics questions. Even if the question does have a good answer, the person who could answer it is not on the site! Anyway, my comment about a user name and profile information still stands - give yourself an identity, even if it is a fake one. Good luck on the bounty (the last two on my questions failed to get an answer).

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Answer 1

It's not clear what you mean by "the R-charge." If you have a U(1) R-symmetry, you can make linear combinations of its charges and those of a non-R U(1) symmetry and get a new R-symmetry. So "values greater than 1/2" are not, generically, special.

At a superconformal fixed point, there is a special U(1) R-symmetry that is part of the superconformal algebra. In this case, R-charges are related to operator dimensions and so are constrained by unitarity bounds. Maybe you have this in mind. The literature on $a$-maximization might be the sort of thing you're looking for.

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Thanks for the insights. Can you may be add some examples of what you say and/or link to some pedagogic/expository writings on this.

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And I didn't get your point about the arbitrariness of the value of the R-charge - isn't there something "canonical" about the statement that the R-charge of a scalar chiral superfield is 1/2? (..and my question is about the alleged scenarios where RG flow apparently seems to cause violation of it - like may be my utterly vague distillation of say this paper - http://arxiv.org/abs/1104.0680

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