Scaling and superscaling solutions from the functional renormalization group

摘要

We study the renormalization group flow of $\mathbb{Z}_2$-invariantsupersymmetric and non-supersymmetric scalar models in the local potentialapproximation using functional renormalization group methods. We focus ourattention to the fixed points of the renormalization group flow of thesemodels, which emerge as scaling solutions. In two dimensions these solutionsare interpreted as the minimal (supersymmetric) models of conformal fieldtheory, while in three dimension they are manifestations of the Wilson-Fisheruniversality class and its supersymmetric counterpart. We also study theanalytically continued flow in fractal dimensions between 2 and 4 and determinethe critical dimensions for which irrelevant operators become relevant andchange the universality class of the scaling solution. We also include novelanalytic and numerical investigations of the properties that determine theoccurrence of the scaling solutions within the method. For each solution weoffer new techniques to compute the spectrum of the deformations and obtain thecorresponding critical exponents.