Anomaly matching for the phase diagram of massless $\mathbb{Z}_N$-QCD

@article{Tanizaki2018AnomalyMF,
  title={Anomaly matching for the phase diagram of massless \$\mathbb\{Z\}\_N\$-QCD},
  author={Yuya Tanizaki and Yuta Kikuchi and Tatsuhiro Misumi and Norisuke Sakai},
  journal={Physical Review D},
  year={2018},
  volume={97},
  pages={054012}
}
We elucidate that the phase diagram of massless $N$-flavor QCD under $\mathbb{Z}_N$ flavor-twisted boundary condition (massless $\mathbb{Z}_N$-QCD) is constrained by an 't Hooft anomaly involving two-form gauge fields. As a consequence, massless $\mathbb{Z}_N$-QCD turns out to realize persistent order at any temperatures and quark chemical potentials, namely, the symmetric and gapped phase is strictly forbidden. This is the first result on the finite-$(T,\mu)$ phase diagram in QCD-type theories… 

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