Higher derivative extension of the functional renormalization group

TL;DR

This paper explores an advanced extension of the functional renormalization group by incorporating higher derivatives, demonstrating that the epsilon expansion near the Wilson-Fisher fixed point is captured within this framework.

Contribution

It introduces a higher derivative extension of the FRG equations and shows their consistency with the epsilon expansion around the Wilson-Fisher fixed point.

Findings

Higher derivative terms are incorporated into the FRG equations.

The epsilon expansion is reproduced by the local potential approximation.

The approach generalizes the FRG framework for scalar fields.

Abstract

We study higher derivative extension of the functional renormalization group (FRG). We consider FRG equations for a scalar field that consist of terms with higher functional derivatives of the effective action and arbitrary cutoff functions. We show that the epsilon expansion around the Wilson-Fisher fixed point is indeed reproduced by the local potential approximation of the FRG equations.