Prediction for Maximum Supercooling in SU(N) Confinement Transition

The thermal confinement phase transition (PT) in $SU(N)$ Yang-Mills theory is first-order for $N\ge 3$, with bounce action scaling as $N^2$. Remarkably, lattice data for the action include a small coefficient whose presence likely strongly alters the PT dynamics. We give evidence, utilizing insights from softly-broken SUSY YM models, that the small coefficient originates from a deconfined phase instability just below the critical temperature. We predict the maximum achievable supercooling in $SU(N)$ theories to be a few percent, which can be tested on the lattice. We briefly discuss the potentially significant suppression of the associated cosmological gravitational wave signals.