Prediction for Maximum Supercooling in SU(N) Confinement Transition

The thermal confinement phase transition in SU ( N ) Yang-Mills theory is first order for N ≥ 3 , with bounce action scaling as N 2 . Remarkably, lattice data for the action include a small coefficient whose presence likely strongly alters the phase transition dynamics. We give evidence, utilizing insights from softly broken supersymmetric Yang-Mills 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.