# How does the generalized effective action in Wetterich's exact RG scheme relate to observables at different scales?

I am not familiar with Wetterich's exact RG paradigm, and cannot understand the main idea behind it. I understand that if one could have solved the model and obtained the all the n-point functions then there would not have been any need for any RG analysis.

The Wilson-Polchinski RG framework (see, for example, arxiv-0702365) extends the ordinary purturbative RG approach beyond perturbative regimes. But it stills adheres to the same general principle: lowering the UV cutoff of the model and tracking the growth of various terms.

In Wettrich's approach (See, for example, arxiv-0005122), a generalized effective action, $$\Gamma_k[\phi]$$ is used, which is the 1PI generating functional with all modes below a momentum scale $$k$$ frozen (i.e., an IR cutoff at the momentum scale $$k$$).

Why is $$\Gamma_{k}[\phi]$$ useful for extracting information about IR physics? (To be more concrete, in Eq. 2.11 on page 17 of arxiv-0005122, it seems one gets back the same source, $$J$$, and not some coarse-grained version.)

• Minor comment to the post (v3): In the future please link to abstract pages rather than pdf files. – Qmechanic Feb 4 at 20:41
• Thanks, @Qmechanic! Will do. – S.G. Feb 4 at 22:42