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Asymptotic freedom requires perturbative renormalizability?

  1. Feb 4, 2016 #1
    I have read many times that a theory (such as gravity) that contains couplings with negative mass dimensions cannot be asymptotically free. Does anyone have a reference that proves that that's the case? The argument is usually just that the coupling grows with energy, as seen in the Callen-Symantek equation. But if that's the argument, then it's hard to see how such a theory could be asymptotically safe either, and plenty of people think that gravity might be asymptotically safe. Thanks so much!
  2. jcsd
  3. Feb 9, 2016 #2
    Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
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