Definition of “quasi-locality” in Wilsonian RG scheme

Question

I’m studying about the holographic RG with this paper.

In that paper they say Wilsonian action expects quasi locality, but I’m not sure what “quasi-locality" exactly means.

If quasi-locality means sth “seems” local but not local exactly, then Wilsonian RG produces some local terms which didn’t appear in classical action?

Also I’m wondering why this property is not appeared in Wheeler-deWitt (WdW) formalism because there is no $\partial_z g_{zz}$ term in action.

Answer 1

1. An ultra-local function $f(x)$ only depends on fields at the spacetime point $x$.

2. A local function $f(x)$ only depends on fields and at most finite many of their spacetime derivatives at the spacetime point $x$.

3. A quasi-local function $f(x)$ only depend on fields in a finite spacetime neighborhood around the spacetime point $x$, cf. e.g. this related Phys.SE post.

The Wilsonian effective action is quasi-local due to the coarse-graining scale $\Lambda=\Lambda_L$, cf. e.g. my Phys.SE answers here and here.