Running couplings with a vanishing scale anomaly

TL;DR

This paper explores how running couplings can originate from spontaneous breaking of exact scale invariance without anomalies, providing a new perspective on scale invariance in quantum field theories.

Contribution

It demonstrates that ordinary quantum field theories can be embedded into scale-invariant models with spontaneous symmetry breaking, recovering standard running behaviors.

Findings

Running couplings can emerge from spontaneous scale symmetry breaking.

Embedding theories with flat directions reproduces standard running.

Scale invariance does not inherently solve cosmological constant issues.

Abstract

Running couplings can be understood as arising from the spontaneous breaking of an exact scale invariance in appropriate effective theories with no dilatation anomaly. Any ordinary quantum field theory, even if it has massive fields, can be embedded into a theory with spontaneously broken exact scale invariance in such a way that the ordinary running is recovered in the appropriate limit, as long as the potential has a flat direction. These scale-invariant theories, however, do not necessarily solve the cosmological constant or naturalness problems, which become manifest in the need to fine-tune dimensionless parameters.