1
$\begingroup$

In QCD, there are quarks at high energies, and pions are composite degrees of freedom that appear at low energy where the quarks are strongly coupled. The pion Lagrangian is non-renormalizable; it breaks down at the QCD scale and must be replaced by the full UV-complete theory of QCD.


Are all effective field theories non-renormalizable quantum field theories which can nonetheless be used to make physical predictions at some energy scales because all but a small number of terms in the Lagrangian are suppressed at these energy scales?

Is the UV completion of a effective field theory a completely new quantum field theory? For example, is the lagrangian of QCD completely different in character than the pion Lagrangian, but reduces to the pion lagrangian at low energies?

$\endgroup$
1
$\begingroup$

There are many possibilities. The chiral lagrangian is a non-renormalizable effective field theory (already at leading order), and is expressed in terms of completely different fields compared to its UV completion QCD.

QCD itself is renormalizable and well defined at arbitrarily high energies, but is presumably also just an effective field theory. This means that we expect higher dimension (non-renormalizable) operators to be present as well.

The rest of the standard model is renormalizable, but not well defined at arbitrarily high energies. This means that it is certainly an effective field theory, and we expect higher dimension operators to exist.

Some EFTs, like the chiral lagrangian, involve new, composite, fields (like the pion). Others, like effective theories near a Fermi surface involve fields that are related by an RG flow to the microscopic fields. We also have EFTs (like NRQED, NRQCD) which involve fields that are related by RG flow to a subset of the original fields.

The only thing that is probably forbidden (by c-theorems, in cases where that can be made rigorous) is to have more low energy fields than high energy fields.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.