What's the difference be Wilsonian and continuum EFT?

Question

In his review on Effective Field Theory, Georgi emphasizes

Within the general framework of the effective field theory idea, there are two rather different approaches, which I will call the Wilson approach, and the continuum effective field theory approach. It is the second of these that I will discuss in detail here. But I should start by explaining why I think that they are different. I will argue that the two take a very different approach to renormalization. In Wilson effective theory, the fundamental question is How does the full theory change as you integrate out high momentum modes and look at it at larger distances? [...] In what I call continuum effective field theory, the question is How do we modify the theory to allow the use of a mass independent scheme and still get the physics right?

A longer discussion of the two perspectives on EFTs was recently here. Unfortunately, I'm not able to understand what Georgi or Rivat are trying to say here.

What exactly is the difference be Wilsonian and continuum EFT? Any help of reference would be greatly appreciated.

Answer 1

In Wilsonian EFT we integrate out higher energy terms (momentum) to obtain a low energy (momentum) field theory of contact terms. This theory can then be used to either produce the RG flow for a specific theory thus getting rid of divergence by modifying coupling constants or it can be used as a low energy expansion of the theory in order to investigate the low energy behaviour of a theory, I heavily advise looking at Dr. Claduia de Rham and Dr. Andrew Tolley's work on using Wilsonian EFTs to constrain regions of possible UV completeness of massive gravity.

In the continuum case, the EFT is valid at all energies provided we specify cut-offs. That is there is a set scale $\Lambda_{min}$ to $\Lambda_{max}$ which we can shift up and down, but we cannot describe the entire range of energies at once. We could investigate low energy interactions or high energy interactions but not both.

So Wilsonian EFTs are great for renormalizing things via changing coupling constants but then we have to go back to the original theory to get any higher energy interactions, where as continuum EFTs are valid at all energies within a specified range about that energy.