Scaling and superscaling solutions from the functional renormalization group

Understand

We study the renormalization group flow of $\mathbb{Z}_2$-invariant supersymmetric and non-supersymmetric scalar models in the local potential approximation using functional renormalization group methods.

• We focus our attention to the fixed points of the renormalization group flow of these models, which emerge as scaling solutions.
• In two dimensions these solutions are interpreted as the minimal (supersymmetric) models of conformal field theory, while in three dimension they are manifestations of the Wilson-Fisher universality class and its supersymmetric counterpart.
• We also study the analytically continued flow in fractal dimensions between 2 and 4 and determine the critical dimensions for which irrelevant operators become relevant and change the universality class of the scaling solution.