Solutions to the reconstruction problem in asymptotic safety
Jul 30, 2015Citations per year
Abstract: (Springer)
Starting from a full renormalised trajectory for the effective average action (a.k.a. infrared cutoff Legendre effective action) Γ , we explicitly reconstruct corresponding bare actions, formulated in one of two ways. The first step is to construct the corresponding Wilsonian effective action S through a tree-level expansion in terms of the vertices provided by Γ . It forms a perfect bare action giving the same renormalised trajectory. A bare action with some ultraviolet cutoff scale Λ and infrared cutoff k necessarily produces an effective average action Γ that depends on both cutoffs, but if the already computed S is used, we show how Γ can also be computed from Γ by a tree-level expansion, and that Γ → Γ as Λ → ∞. 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 Γ and S .Note:
- 32 pages
- Renormalization Group
- Models of Quantum Gravity
- effective action
- tree approximation
- trajectory
- infrared
- asymptotic safety
- ultraviolet
- partition function
- duality
References(43)
Figures(1)
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