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I have asked this question on physics stackexchange and been met with a deafening silence. So I will try it here. From the modern point of view about renormalization ,super-renormalizable terms are not as innocent as they may seem. This is what I am not sure I understand and would like clarity. Is this because from the point of view of some UV theory when we let the rg flow the "relevant" operators get multiplied by positive powers of the cut off in the lower energy theory but this is bad because the cut-off can be made as high as needed and so we end up with couplings that can be made large in the lower energy theory where supposedly perturbation theory was valid? If the above is correct does this mean that there is some fine-tuning in the high and or low energy theory, or does this mean the Lagrangian in the high energy theory has a symmetry that forbids these "relevant" operators.

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  • $\begingroup$ FYI the correct expression is "deafening silence." $\endgroup$ – ಠ_ಠ Oct 24 '16 at 0:35
  • $\begingroup$ thanks for the correction, it's fixed now. But if no answers come it will be deadening silence $\endgroup$ – Amara Oct 24 '16 at 2:55
  • $\begingroup$ I think what you say is more or less correct, the relevant operators makes the RG flow unstable because even a little perturbation in the UV gets polynomially amplified as one runs in the IR. How can one thus reach a hierarchically separated IR fixed point? One should fine-tune the initial conditions of the RG trajectory. The presence of a symmetry doesn't remove the fine-tuning, it just gives you rational for it, so that one does not see it as an unnatural feature of theory. With no symmetry there is little or no clue about why the special IR was obtained by such special UV initial condition $\endgroup$ – TwoBs Oct 26 '16 at 22:30
  • $\begingroup$ Relevant terms (at the UV fixed point) are the super-renormalizable ones if one is trying to remove the cut-off. The point is that one is going backwards against the flow of the RG so these couplings become small in the UV, and exponentially so in the number of RG steps. The next best thing is just-renormalizable terms with asymptotic freedom. $\endgroup$ – Abdelmalek Abdesselam Nov 8 '16 at 23:06

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