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

Jingxu Wu, Chenjia Li, Jie Shi

TL;DR

The paper develops a self-consistent dark-QCD chiral-transition framework that preserves a $Z(3)$ center structure in the Polyakov-loop sector and couples it to a chiral order parameter $σ$, enabling a closed chain from vacuum landscape to metastability, domain-wall physics, and bubble nucleation. It characterizes the homogeneous vacuum structure and identifies a metastability window bounded by a spinodal line, then constructs $Z(3)$ domain walls with chiral backreaction to extract wall thickness and surface tension. The dynamics of metastable decay are connected to thermal nucleation through the thin-wall relations $R_c(T)=2Σ(T)/ΔV(T)$ and $S_3(T)/T = (16π/3) Σ(T)^3 /(T ΔV(T)^2)$, using outputs derived from the same effective potential $V_{eff}(σ,ℓ;T)$ to ensure consistency. This framework provides a reproducible, modular pipeline for extensions to full multi-field bounce calculations and potential dark-sector cosmological applications.

Abstract

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 $S_3(T)/T$ 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.

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

TL;DR

The paper develops a self-consistent dark-QCD chiral-transition framework that preserves a center structure in the Polyakov-loop sector and couples it to a chiral order parameter , enabling a closed chain from vacuum landscape to metastability, domain-wall physics, and bubble nucleation. It characterizes the homogeneous vacuum structure and identifies a metastability window bounded by a spinodal line, then constructs domain walls with chiral backreaction to extract wall thickness and surface tension. The dynamics of metastable decay are connected to thermal nucleation through the thin-wall relations and , using outputs derived from the same effective potential to ensure consistency. This framework provides a reproducible, modular pipeline for extensions to full multi-field bounce calculations and potential dark-sector cosmological applications.

Abstract

We present a self-contained theoretical analysis of a dark-QCD chiral transition in which the Polyakov-loop sector retains an explicit 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 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 and the nucleation exponent 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.
Paper Structure (6 sections, 54 equations, 6 figures)

This paper contains 6 sections, 54 equations, 6 figures.

Table of Contents

  1. Introduction
  2. Minimal coupled $(\sigma,\ell)$ effective theory and variational equations
  3. Homogeneous vacuum structure, metastability window, and spinodal criterion
  4. Z(3) Domain Walls with Chiral Backreaction: Profiles and Surface Tension
  5. Metastable bubbles and nucleation barrier: $R_c(T)$ and $S_3(T)/T$
  6. Conclusions

Figures (6)

  • Figure 1: Schematic visualization of the Polyakov-loop sector potential: the cubic invariant in \ref{['eq:VZ3']} generates the $Z(3)$ three-branch structure, while the explicit breaking term \ref{['eq:Vbreak']} biases the branches and enables metastability. (Actual plots will be provided in Sec. \ref{['sec:homog']} once parameters are fixed.)
  • Figure 2: Temperature dependence of homogeneous order parameters in the coupled $(\sigma,\ell)$ theory.
  • Figure 3: Vacuum splitting and spinodal criterion. The metastability window ends when the smallest Hessian eigenvalue at the metastable minimum vanishes.
  • Figure 4: Z(3) domain-wall profiles with chiral backreaction.
  • Figure 5: Surface tension and thickness of the Z(3) wall across the metastability window.
  • ...and 1 more figures