Vanishing trace anomaly in flat spacetime

TL;DR

This paper introduces a quantum scale invariant regularization approach that preserves scale symmetry at the quantum level in certain nonrenormalizable models, challenging the usual understanding of scale symmetry violation.

Contribution

It demonstrates how quantum scale invariant regularization can maintain scale symmetry despite non-zero RGE functions, offering a new perspective on quantum scale invariance.

Findings

Scale symmetry remains unbroken at the quantum level.

The regularization method can be applied with various regularization schemes.

Explicit analysis using a scalar field toy model supports the theoretical claims.

Abstract

Quantum scale invariant regularization is a variant of dimensional regularization where the renormalization scale is treated as a dynamical field. But, rather than be regarded as a novel regularization method on par with dimensional regularization, momentum cutoff, Pauli-Villars etc., it should be understood as a way to define a subset in the infinite space of nonrenormalizable models of certain type. The subset realizes the demand that renormalization scale, along with any other dimensionful parameters, should be interpreted as a dynamical field's homogeneous background. This restriction is most straightforwardly implemented using dimensional regularization but it can hypothetically be imposed with any regularization method. Theories that satisfy it offer a new perspective on the radiative violation of global scale symmetry associated with RGE functions. As a result of the quantum scale invariant regularization being implemented, the scale symmetry is preserved at the quantum level despite the RGE functions being non-zero, as can be inspected at the level of composite quantum operators that govern dilatation of Green functions. We analyze these statements in explicit detail using a specific but easily generalized toy model with scalar fields.