Domain Walls From Confining Bubbles: $SU(N_{c})$ Yang Mills at Finite $θ$

We study the confinement phase transition in SU($N_{c}$) pure Yang-Mills theory at finite $\theta \neq 0$ using the Improved Holographic QCD (IHQCD) model. We show that the critical temperature, as a function of $\theta$ for large but fixed $N_{c}$, is reduced, thus decreasing the amount of supercooling in the confinement phase transition. Upon completion of the confinement phase transition, a network of domain walls can be produced, owing to the multi-branched vacuum structure of Yang-Mills theory at finite $\theta$. We highlight the potential interplay between the produced domain walls and the confinement phase transition dynamics. We emphasize that DW production from bubble coalescence in strongly coupled non-conformal FOPTs is a dynamical process of vacuum assignment, hydrodynamics, and local reheating effects, all potentially affecting the approach towards the scaling regime. Lastly, we demonstrate the level of tuning necessary for potentially interesting imprints from gravitational waves through domain wall annihilation and its interplay with the confinement PT.