7 research outputs found
Solutions to the reconstruction problem in asymptotic safety
Starting from a full renormalised trajectory for the effective average action
(a.k.a. infrared cutoff Legendre effective action) , we explicitly
reconstruct corresponding bare actions, formulated in one of two ways. The
first step is to construct the corresponding Wilsonian effective action
through a tree-level expansion in terms of the vertices provided by .
It forms a perfect bare action giving the same renormalised trajectory. A bare
action with some ultraviolet cutoff scale and infrared cutoff
necessarily produces an effective average action that
depends on both cutoffs, but if the already computed is used, we
show how can also be computed from by a
tree-level expansion, and that as
. Along the way we show that Legendre effective actions with
different UV cutoff profiles, but which correspond to the same Wilsonian
effective action, are related through tree-level expansions. All these
expansions follow from Legendre transform relationships that can be derived
from the original one between and .Comment: 32 page