Does Renormalization group tell you if a theory is Renormalizable or not ?

[zetafunction]

Does Renormalization group tell you if a theory is Renormalizable or not ??

the idea is this, using the Renormalization group equation for our theory (QED, Gravity, Gauge theories..) can tell this RG equation if our theory is renormalizable or not for big or small energies ??

 

[ExactlySolved]

No, if the theory is non-renormalizable then by definition there is no RG equation for that theory.

 

[zetafunction]

but you would not know if a given theory is renormalizable or not 'a priori' so perhas you could obtain a renormalization group equation or similar, for example i think there is a RG equation fro gravity..

 

[atyy]

but you would not know if a given theory is renormalizable or not 'a priori' so perhas you could obtain a renormalization group equation or similar, for example i think there is a RG equation fro gravity..

The RG can tell you if the theory has a continuum limit, and that's what's being asked for gravity. For a continuum limit to exist, the RG equation must have a UV fixed point. If a continuum limit exists, then the theory is renormalizable.

However, there are renormalizable theories that don't have continuum limits, such as QED. The QED fixed point is infrared, not UV. I don't understand the relationship (if any?) between renormalizability and an infrared fixed point.