On Wikipedia it says that the two peculiar properties of quantum chromodynamics (QCD) are: confinement and asymptotic freedom.

Asymptotic freedom is the idea that at low energies we cannot use perturbation theory because the coupling becomes extremely strong. One the other hand, at sufficiently high energies, the coupling becomes very small and so we can use perturbation theory. This can all be determined by investigating the $\beta$-function.

My question is:

Why is the asymptotic freedom of quarks not considered to be a sufficient explanation for confinement?

My logic:

According to asymptotic freedom: at low energies the coupling becomes so strong that quarks cannot be isolated which explains confinement. If I am right (which I'm probably not), then why is confinement still considered to be such a mystery?


1 Answer 1


It's not a sufficient explanation. There are asymptotically free theories which are not strongly coupled in the IR.

The rate at which the coupling gets strong is important. In QCD, it seems to get strong very quickly near the confinement scale, so that beyond a certain scale, you only see hadrons. It is not really understood how this works. The perturbation theory suggests it could happen, as you've observed, but one can not trust perturbation theory at strong coupling.

  • 1
    $\begingroup$ Very familiar with the kondo effect $\endgroup$
    – Nogueira
    May 2, 2016 at 3:37
  • $\begingroup$ +1 Are asymptotic freedom+strong coupling in IR and confinement the two sides of the same coin? $\endgroup$
    – Diracology
    Apr 17, 2018 at 17:47
  • $\begingroup$ But are there confining theories which are not asymptotically free? $\endgroup$ Nov 22, 2021 at 15:11

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