Scale and confinement phase transitions in scale invariant $SU(N)$ scalar gauge theory

TL;DR

This paper investigates the nature of scale and confinement phase transitions in $SU(N)$ scalar gauge theories, revealing that the scale transition is first-order and that the Polyakov loop significantly influences the latent heat, impacting gravitational wave predictions.

Contribution

It introduces an effective field theory approach including the Polyakov loop to study scale and confinement phase transitions in $SU(N)$ scalar gauge theories for N=3,4,5,6, highlighting the first-order nature and the impact on latent heat.

Findings

Scale phase transition is first-order for N=3,4,5,6.

Polyakov loop increases latent heat in some cases.

Potential implications for gravitational wave signals from early universe.

Abstract

We consider scalegenesis, spontaneous scale symmetry breaking, by the scalar-bilinear condensation in $SU(N)$ scalar gauge theory. In an effective field theory approach to the scalar-bilinear condensation at finite temperature, we include the Polyakov loop to take into account the confinement effect. The theory with $N=3,4,5$ and $6$ is investigated, and we find that in all these cases the scale phase transition is a first-order phase transition. We also calculate the latent heat at and slightly below the critical temperature. Comparing the results with those obtained without the Polyakov loop effect, we find that the Polyakov effect can considerably increase the latent heat in some cases, which would mean a large increase in the energy density of the gravitational waves background, if it were produced by the scale phase transition.