Solutions to the reconstruction problem in asymptotic safety

Understand

Starting from a full renormalised trajectory for the effective average action (a.k.a.

• infrared cutoff Legendre effective action) $\Gamma_k$, we explicitly reconstruct corresponding bare actions, formulated in one of two ways.
• The first step is to construct the corresponding Wilsonian effective action $S^k$ through a tree-level expansion in terms of the vertices provided by $\Gamma_k$.
• It forms a perfect bare action giving the same renormalised trajectory.