Z(3) Metastable Bubbles and Chiral Dynamics Across a Dark-QCD Deconfinement Transition

We present a self-contained theoretical analysis of a dark-QCD chiral transition in which the Polyakov-loop sector retains an explicit $Z(3)$ structure and couples consistently to the chiral order parameter.Working within a coupled chiral–Polyakov effective theory, we map the homogeneous vacuum landscape and identify a metastability window bounded by spinodal loss of stability.We then construct $Z(3)$ domain-wall solutions including chiral backreaction, extracting temperature-dependent wall profiles and surface tension.Finally, we connect homogeneous metastability and wall microphysics to thermal bubble nucleation by evaluating the critical radius $R_c(T)$ and the nucleation exponent $S_3(T)\mathrm{/}T$ in the thin-wall regime, providing a compact set of reproducible diagnostics for the decay of the metastable phase.Our results establish a coherent pipeline from vacuum structure to nonperturbative interfaces and nucleation barriers, suitable for systematic extensions to full multi-field bounce calculations and dark-sector cosmological applications.