In the context of the standard model, I got the impression that gauge field theories are considered fundamental, and effective field theories can be derived from them for certain energy scales.

But could it also be the other way around, that sometime in the future we find a non-gauge theory that has a set of apparent tuning parameters, of which the masses and the coupling strengths of the current standard model derive (at least around some operating point)?

As a visual example: fluid dynamics is an effective field theory when the fluid is viewed as being composed of atoms and molecules. But could it be that we once find out that elementary particles can be described more fundamentally by a kind of "fancy" generalization of fluid dynamics?

As a further motivation: think of the dual superconductor model of QCD or Gamow's liquid drop model of the nucleus . What if nuclear physics had stopped there? And who can say when it's time to stop looking for more fundamental theories?

Is there some compelling argument against such kind of speculation?

  • $\begingroup$ I'm not sure why you say "gauge theories are considered fundamental". Usually the marker for a fundamental vs. effective quantum field theory is renormalizability (i.e. non-renormalizable theories must necessarily be seen as effective), not whether or not it involves gauge fields. $\endgroup$
    – ACuriousMind
    Apr 8 '21 at 17:16
  • $\begingroup$ @ACuriousMind: I am still learning (and probably always will...) I just got the impression that gauge theories are considered fundamental. If that's wrong, that would be part of the answer. $\endgroup$
    – oliver
    Apr 8 '21 at 17:25

Being a gauge theory and being an effective theory are completely orthogonal concepts.

An effective quantum field theory is a theory that is only valid up to some energy scale. These theories are often non-renormalizable, but since they possess a physical meaningful energy cutoff, this is not a problem. Conversely, a (candidate for) a "fundamental" quantum field theory is one that is renormalizable, so that it does not have to have an energy scale beyond which it is necessarily invalid.

So you can look at a theory, see that it is non-renormalizable, and conclude that it is not fundamental, but you cannot deduce from it being renormalizable that it's not an effective theory.

There is nothing about effective theories that would forbid them being gauge theories, and you can conceivably have a theory that only becomes a gauge theory in some effective regime - there might be a single term in the Lagrangian that spoils gauge symmetry that becomes irrelevant in some effective limit.

  • $\begingroup$ So I am trying to rephrase it: there is no known hard reason why a supposed fundamental theory need to be a gauge theory (except for some effective regimes that correspond to today's standard model), right? Of course, except that such a theory would have to explain conservation of charges, but other than that... $\endgroup$
    – oliver
    Apr 8 '21 at 21:13
  • 1
    $\begingroup$ @oliver Depends on what you mean by "fundamental". There is no reason a renormalizable theory has to be gauge. There are good reasons the SM, as the "most fundamental QFT" describing world excluding gravity, is formulated as a gauge theory. But due to the non-renormalizability of QFTs with gravity, people do not believe that the "fundamental" that describes our world is a QFT at all. Whether or not QG will be a "gauge theory" is meaningless. Also, "gauge theory" is not inherent in a system, see physics.stackexchange.com/q/13870/50583, physics.stackexchange.com/q/257018/50583 $\endgroup$
    – ACuriousMind
    Apr 8 '21 at 21:26
  • $\begingroup$ Thanks for these very interesting references! I am always surprised to find that there are so many subtle and equally important facts I have never heard about. $\endgroup$
    – oliver
    Apr 8 '21 at 21:38

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