Limit of vanishing regulator in the functional renormalization group

TL;DR

This paper investigates the behavior of the functional renormalization group as the regulator amplitude approaches zero, highlighting its implications for symmetry preservation and scheme equivalence.

Contribution

It analyzes the limit of vanishing regulator amplitude in the functional renormalization group, connecting it to the pseudo-regulator and symmetry considerations.

Findings

Limit of regulator amplitude a→0 relates to pseudo-regulators.

This limit helps eliminate symmetry breaking caused by the regulator.

The approach is not ideal for high-precision calculations.

Abstract

The non-perturbative functional renormalization group equation depends on the choice of a regulator function, whose main properties are a "coarse-graining scale" $k$ and an overall dimensionless amplitude $a$. In this paper we shall discuss the limit $a\to0$ with $k$ fixed. This limit is closely related to the pseudo-regulator that reproduces the beta functions of the $\overline{\text{MS}}\,$ scheme, that we studied in a previous paper. It is not suitable for precision calculations but it appears to be useful to eliminate the spurious breaking of symmetries by the regulator, both for nonlinear models and within the background field method.