Functional Renormalization and $\overline{\text{MS}}$

TL;DR

This paper introduces a regulator choice in the functional renormalization group that reproduces dimensional regularization results at one and two loops, extending the ar scheme nonperturbatively while preserving symmetries.

Contribution

It proposes a regulator within the functional renormalization group that replicates ar scheme results and maintains nonlinear symmetries, applicable across dimensions.

Findings

Reproduces ar scheme results at one and two loops

Recovers all multicritical models in two dimensions

Preserves nonlinear symmetries

Abstract

Working with scalar field theories, we discuss choices of regulator that, inserted in the functional renormalization group equation, reproduce the results of dimensional regularization at one and two loops. The resulting flow equations can be seen as nonperturbative extensions of the $\overline{\text{MS}}\,$ scheme. We support this claim by recovering all the multicritical models in two dimensions. We discuss a possible generalization to any dimension. Finally, we show that the method also preserves nonlinearly realized symmetries, which is a definite advantage with respect to other regulators.