Scale Symmetry Spontaneously Broken by Asymptotic Behavior

TL;DR

This paper investigates models with global scale invariance, showing that scale symmetry is spontaneously broken due to singular infrared behavior of conserved currents, influencing the theory's structure and potential flatness.

Contribution

It introduces new models with global scale invariance that allow nontrivial potentials and demonstrates spontaneous symmetry breaking via infrared singularities.

Findings

Conserved currents are singular in the infrared, preventing conserved charges.

Scale symmetry influences the structure and flatness of potentials.

Models exhibit spontaneous breaking of scale symmetry due to infrared behavior.

Abstract

Conserved quantities are obtained and analyzed in the new models with global scale invariance recently proposed. Such models allow for non tivial scalar field potentials and masses for particles, so that the scale symmetry must be broken somehow. We get to this conclusion by showing that the infrared behavior of the conserved currents is singular so that there are no conserved charges associated with the global scale symmetry. The scale symmetry plays nevertheless a crucial role in determining the structure of the theory and it implies that in some high field regions the potentials become flat.