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Could a theory that looks like an effective field theory also be fundamental?

Physics Asked on June 2, 2021

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?

One Answer

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.

Correct answer by ACuriousMind on June 2, 2021

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