Gravitational Waves from Confinement in $SU(N)$ Yang-Mills Theory

TL;DR

This paper analyzes the gravitational wave signals produced by confinement phase transitions in $SU(N)$ Yang-Mills theory, incorporating lattice data and large-$N$ scaling to predict the strength and characteristics of these signals.

Contribution

It introduces a detailed framework combining lattice data, effective Polyakov loop models, and large-$N$ scaling to predict gravitational wave spectra from $SU(N)$ confinement transitions.

Findings

Gravitational wave signals are strongest at $N=20$.

Thin-wall approximation is valid at small $N$ but breaks down at large $N$.

Predicted signals are generally weak across all $N$.

Abstract

We provide a detailed analysis of the gravitational wave spectrum of $SU(N)$ pure Yang-Mills theory. The confinement phase transition is described with an effective Polyakov loop model, using the latest lattice data as an input. In particular, recent lattice studies clarified the large-$N$ scaling of the surface tension, which we incorporate through a modification of the kinetic term. We demonstrate that the thin-wall approximation agrees with the Polyakov loop model at small $N$ while it breaks down at large $N$. Furthermore, we include reliable estimates of the bubble wall velocity using a recently developed framework based on a large enthalpy jump at the phase transition. Altogether, this allows us to derive the gravitational wave signals for all $SU(N)$ confinement phase transitions and clarifies the behaviour at large $N$. The strongest signal arises for $N=20$, but overall the predicted signals remain rather weak. Our work paves the way for future studies of other gauge groups and systems with fermions.