Functional renormalization group with a compactly supported smooth regulator function

TL;DR

This paper introduces a compactly supported smooth (CSS) regulator function for the functional renormalization group, demonstrating its versatility and effectiveness in studying critical phenomena in quantum field theories.

Contribution

It presents a new CSS regulator that generalizes existing regulators, recovers optimized forms in certain limits, and applies it to analyze critical behavior in quantum electrodynamics and scalar theories.

Findings

CSS regulator recovers optimized regulator in a specific limit

It reduces to exponential and power-law regulators in appropriate limits

Successfully applied to study critical phenomena in quantum field theories

Abstract

The functional renormalization group equation with a compactly supported smooth (CSS) regulator function is considered. It is demonstrated that in an appropriate limit the CSS regulator recovers the optimized one and it has derivatives of all orders. The more generalized form of the CSS regulator is shown to reduce to all major type of regulator functions (exponential, power-law) in appropriate limits. The CSS regulator function is tested by studying the critical behavior of the bosonized two-dimensional quantum electrodynamics in the local potential approximation and the sine-Gordon scalar theory for d<2 dimensions beyond the local potential approximation. It is shown that a similar smoothing problem in nuclear physics has already been solved by introducing the so called Salamon-Vertse potential which can be related to the CSS regulator.