Consistency of Wilsonian effective actions

TL;DR

This paper explores the properties and constraints of Wilsonian effective actions, showing they satisfy certain consistency and convexity conditions and can be used to derive restrictions on cutoff schemes and reparametrizations.

Contribution

It demonstrates that Wilsonian effective actions, derived from two-particle-irreducible functionals, inherently satisfy perturbative and non-perturbative conditions, providing a framework for analyzing their properties.

Findings

Wilsonian actions satisfy perturbative consistency conditions.

Wilsonian actions obey non-perturbative convexity conditions.

Restrictions on cutoff schemes and reparametrizations can be derived from Wilsonian actions.

Abstract

Wilsonian effective actions are interpreted as free energies in ensembles with prescribed field expectation values and prescribed connected two-point functions. Since such free energies are directly obtained from two-particle-irreducible functionals, it follows that Wilsonian effective actions satisfy elementary perturbative consistency conditions, and non-perturbative convexity conditions. In particular, the exact determination of a Wilsonian action by other means (e.g. supersymmetry) allows one to extract restrictions on the particular cutoff scheme and field reparametrization that would lead to such a Wilsonian action from an underlying microscopic action.