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Renormalization of the R-charge?

+ 4 like - 0 dislike
32 views

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!

This post has been migrated from (A51.SE)
asked Feb 29, 2012 in Theoretical Physics by user6818 (955 points) [ no revision ]
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).

This post has been migrated from (A51.SE)
@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.

This post has been migrated from (A51.SE)
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...

This post has been migrated from (A51.SE)

1 Answer

+ 5 like - 0 dislike

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.

This post has been migrated from (A51.SE)
answered Mar 8, 2012 by Matt Reece (1,630 points) [ no revision ]
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

This post has been migrated from (A51.SE)
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.

This post has been migrated from (A51.SE)

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