# Roberge-Weiss transitions at different center symmetry breaking patterns in a $\mathbb{Z}_{3}$-QCD model

## TL;DR

This paper investigates how the Roberge-Weiss transition in a $ ext{Z}_3$-QCD model varies with different patterns of center symmetry breaking, revealing the transition's sensitivity to symmetry breaking parameters and implications for deconfinement.

## Contribution

It provides a detailed analysis of the dependence of RW transitions on center symmetry breaking patterns and quark mass non-degeneracy in a $ ext{Z}_3$-QCD model, highlighting the transition's sensitivity to these factors.

## Key findings

- RW transition occurs at specific $ heta_{RW}$ depending on symmetry breaking parameters.
- Transition strength increases as the symmetry breaking parameter $C$ decreases.
- RW transition is more sensitive to deviations in $C$ than to quark mass non-degeneracy.

## Abstract

We study how the Roberge-Weiss (RW) transition depends on the pattern of center symmetry breaking using a $\mathbb{Z}_{3}$-QCD model. We adopt flavor-dependent quark imaginary chemical potentials, namely $(\mu_{u},\mu_{d},\mu_{s})/iT=(\theta-2\pi{C}/3,\,\theta,\,\theta+2\pi{C}/3)$ with $C\in[0,1]$. The RW periodicity is guaranteed and the center symmetry of $\mathbb{Z}_{3}$-QCD is explicitly broken when $C\neq{1}$ or/and quark masses are non-degenerate. For $N_{f}=3$ and $C\neq{1}$, the RW transition occurs at $\theta=\theta_{RW}=(2k+1)\pi/3\,(k\in\mathbb{Z})$, which becomes stronger with decrease of $C$. When $C={1}$, the $\theta_{RW}$ turns into $2k\pi/3$ for $N_{f}=2+1$, but keeps $(2k+1)\pi/3$ for $N_{f}=1+2$; in both cases, the RW transitions get stronger with the mass mismatch. For other $C\neq{0}$ cases, the $\theta_{RW}$'s are not integral multiples of $\pi/3$. We find that the RW transition is more sensitive to the deviation of $C$ from one compared to the mass non-degeneracy and thus the strength of the traditional RW transition with $C=0$ is the strongest. The nature of RW endpoints and its implications to deconfinement transition are investigated.