Renormalization group for effective field theories: cutoff schemes and universality

TL;DR

This paper explores how cutoff schemes affect universality in effective field theories, showing that certain schemes like sharp cutoff perform better and that some universality persists even off criticality.

Contribution

It quantifies cutoff scheme dependence in scalar field theory and compares the effectiveness of different cutoff schemes in preserving universality.

Findings

Sharp cutoff scheme performs better than smooth cutoffs.

Universality persists even in the massive, off-critical case.

Cutoff scheme dependence is quantified by three parameters at two-loop order.

Abstract

In effective field theories, the concept of renormalization of perturbative divergences is replaced by renormalization group concepts such as relevance and universality. Universality is related to cutoff scheme independence in renormalization. Three-dimensional scalar field theory with just the quartic coupling is universal but the less relevant sextic coupling introduces a cutoff scheme dependence, which we quantify by three independent parameters, in the two-loop order of perturbation theory. However, reasonable schemes only allow reduced ranges of those parameters, even contrasting the sharp cutoff with very smooth cutoffs. The sharp cutoff performs better. In any case, the effective field theory possesses some degree of universality even in the massive case (off criticality).