Bags and Confinement Governed by S.S.B. of Scale Invariance

TL;DR

This paper presents a scale-invariant, coordinate-invariant theory where confinement of gauge fields emerges from spontaneous symmetry breaking of scale invariance, leading to different gauge dynamics inside and outside 'bags' with varying vacuum energy densities.

Contribution

It introduces a novel model using two measures and a dilaton to realize spontaneous scale symmetry breaking, resulting in a natural mechanism for confinement and deconfinement phases.

Findings

Gauge dynamics is confining in regions of low vacuum energy density.

Gauge dynamics is non-confining in regions of high vacuum energy density.

The model has a well-defined flat space limit.

Abstract

A general coordinate invariant theory is constructed where confinement of gauge fields and gauge dynamics in general is governed by the spontaneous symmetry breaking (s.s.b.) of scale invariance. The model uses two measures of integration in the action, the standard $\sqrt{-g}$ where $g$ is the determinant of the metric and another measure $\Phi$ independent of the metric. To implement scale invariance (S.I.), a dilaton field is introduced. Using the first order formalism, curvature ( $\Phi R$ and $\sqrt{-g}R^{2}$ ) terms , gauge field term and dilaton kinetic terms are introduced in a conformally invariant way. Exponential potentials for the dilaton break down (softly) the conformal invariance down to global scale invariance, which also suffers s.s.b. after integrating the equations of motion. The model has a well defined flat space limit. As a result of the s.s.b. of scale invariance phases with different vacuum energy density appear. Inside the bags, that is in the regions of larger vacuum energy density, the gauge dynamics is normal, that is non confining, while for the region of smaller vacuum energy density, the gauge field dynamics is confining. Likewise, the dynamics of scalars, like would be Goldstone bosons, is suppressed inside the bags.